i

Experimental Process Development for Scanning

Thermal Microscopy in Air and Vacuum

Sai Kan Tam

MSc by Research

University of York

Physics

February 2017

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Abstract

This thesis explores the procedure of making thermal and force measurements using a

scanning thermal microscope (SThM) in both air and vacuum environments. The atomic force

microscopy(AFM) and SThM literature will be reviewed, including thermal transport at the tip

sample interface and methods of determining the spring constant of the cantilever. The thesis

will then discuss the instruments that are used in the experiment, and the procedure for making

thermal and force measurements. Thermal and force measurements were obtained with five

different samples that cover different thermal and mechanical properties. Silicon, silicon

carbide, mica and PTFE along with a thin film of gold for which the thermal conductivity

would be determined. The topography analysis, interpretation of force and thermal curves will

be discussed and recommendations made about the best ways to attempt quantitative

measurements using these techniques.

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Contents

Abstract ...................................................................................................................................... ii

Content ...................................................................................................................................... iii

List of Tables ............................................................................................................................. v

List of Figures ........................................................................................................................... vi

Acknowledgement ................................................................................................................... xii

Declaration ............................................................................................................................. xiii

Chapter 1 Introduction ......................................................................................................................... 1

1.1. Motivation and Introduction ........................................................................................ 1

1.2. Atomic Force Microscopy ............................................................................................ 4

1.3. Scanning Thermal Microscopy ..................................................................................... 7

1.4. Objectives of this project ........................................................................................... 12

Chapter 2 Principle of force and temperature measurements using scanning probes ............... 13

2.1. Heat Transport in SThM ............................................................................................. 13

2.2. Characteristics of a force curve measured by AFM. ................................................. 18

2.3. Characteristic of a thermal measurement and thermal calibration ............................ 24

Chapter 3 Experimental Method ...................................................................................................... 29

Part I: Instrumentation and preparation ................................................................................... 29

3.1. SThM instrumentation and integration to AFM ......................................................... 29

3.2. Sample selection ......................................................................................................... 34

Part II: Experimental procedures ............................................................................................. 36

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3.3. Preparation for the force and thermal measurements ................................................. 36

3.4. Methods of topography measurements ....................................................................... 40

3.5. Force measurement and roughness procedure ............................................................ 44

3.6. Calibration of thermal probe and measurements procedure ....................................... 47

Chapter 4 Topography and force curves measured using contact mode and thermal probes .. 54

4.1. Physical dimensions from SEM and spring constant results ..................................... 55

4.2. Topography and roughness analysis .................................................................................. 60

4.3. Force measurements comparison between samples .................................................. 68

4.4. Discussion of the results ............................................................................................ 75

Chapter 5 SThM for thermal conductivity measurements ............................................................ 78

5.1. Thermal calibration and probe signal from the data logger ....................................... 78

5.2. Thermal map and the thermal measurements ............................................................ 88

5.3. Discussion and interpretation of thermal results and thermal conductivity ............ 108

Chapter 6 Conclusion and further developments ......................................................................... 116

List of reference ................................................................................................................................ 122

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List of tables

Table 3.1 A table summarising the properties of the materials chosen for this thesis. The table

includes the thermal conductivity, hardness and the elastic modulus of the

samples. [35], [36], [37], [38] ............................................................................. 34

Table 4.1 Dimension measurements and spring constant calculation for all the probes. [35],

[36], [38] .............................................................................................................. 56

Table 4.2 Summary of the topography of each material. ........................................................ 67

Table 4.3 Table presenting the sensitivity a from inverting the overall average slope of silicon

carbide. ................................................................................................................. 68

Table 4.4 Retract force measurements using thermal probes. ................................................ 72

Table 5.1 Table of the conversion coefficient of the thermal probes used in thermal

measurements. ...................................................................................................... 86

Table 5.2 Table of temperature measurements from the thermal probe in air, with a current of

0.8mA. .................................................................................................................. 97

Table 5.3 Table of temperature measurements from the thermal probe in vacuum, with a

current of 0.8mA. ............................................................................................... 103

Table 5.4 Table of temperature measurements from thermal probe, measured in 0.8mA. .. 105

Table 5.5. A summary table for overall the data. The table showed the material, the thermal

conductivity, the elastic modulus, the retract force, the change in temperature for

approach, retract and for the data logger. The new elements are the deformation

column, where measuring the temperature dropped after the tip deforms the sample.

The percentage heat loss is calculating the percentage ratio of approach to data

logger. ................................................................................................................ 109

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List of figures

Figure 1.1 A generic diagram of the main parts of an atomic force microscope, it consists of

a piezoelectric tube as the main driver of the specimen, a laser and a photodiode

for feedback system a cantilever for scanning. [10] ............................................ 4

Figure 1.2 a) A conventional AFM topography image of a gold sample along with b) the

associated thermal image. The conversion coefficient for the scale bar to voltage

is 2.34Å/V. ........................................................................................................... 7

Figure 1.3 a) A typical shape of a fabricated probe. b) shows the structure of a Wollaston wire.

[18] ....................................................................................................................... 9

Figure 2.1 A schematic diagram showing the thermal pathways of a probe in contact with a

sample. a) This diagram shows the SThM operating in ambient environment. The

setup is the probe when operating in active mode. The heat flow is directed from

the probe to the sample. The heat transport by air, Ggas is also shown in the

diagram. Note that Ggas does not exist when the setup is operating in vacuum. b)

A detailed diagram of the dotted circle area in figure 2.1a), showing the heat flow

paths from the tip to the sample. In both the environments, the heat transported

by the radiation Grad and by mechanical contact Gmc exist. The blue area in the

ambient environment represents the water droplets formed by condensation. The

heat transport via water is represented by Gw. Note that Gw does not exist in

vacuum. The diagrams are modified from Poon [25] presentation. ................. 13

Figure 2.2. A typical force measurement diagram of SiC sample and operated in air. The

diagram described the probe position at each point from the starting position

where the probe starts recording the data, approaching to contact point where the

probe makes contact with the sample surface. The tip keeps pressing on until the

tip stop at the pre-set displacement range labelled as tip stopping point. The tip

will then retract from the surface, the surface adhesive force is keeping the tip on

the surface and bending the cantilever, a hysteresis is formed during the tip is

retracting. When the tip gained enough force that overcomes the surface force,

the tip will snap out and retract to the starting position. .................................... 19

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Figure2.3. Schematic diagram of force displacement curve. V0 is the reference voltage when

the tip is away from the surface and the sample is exerting no force on it. The

optical lever sensitivity α is measured at the retract regime, note that the

sensitivity is the inverse of the gradient at the retract curve. [29] ..................... 21

Figure 2.4 A schematic diagram demonstrating the reference cantilever method using a large-

scale cantilever against the AFM cantilever. a) The AFM cantilever is pressed on

a large-scale cantilever that has known property. b) When a force is applied by

the AFM cantilever, both cantilevers will bend as different rate, since both

cantilevers are exerting the same force, the spring constant is measured by the

deflection of the cantilever. [33] ........................................................................ 23

Figure 2.5 A schematic thermal measurement of SiC in air using a fabricated resistor probe

in active mode. The arrows indicate the motion and position of the probe

throughout the measurement. The position at which the probe snaps into the

surface is marked as the contact point. ............................................................. 24

Figure 2.6 A typical thermal result of SiC measured in vacuum operated in active mode. The

main characteristic is there is no heat loss before the tip reaches the contact point.

............................................................................................................................ 25

Figure 2.7 A force curve and a thermal curve to verify the interpretation of the thermal curve.

The intersection of both curves at the contact point and the snap out point are used

to verify the temperature change on the thermal curve. .................................... 26

Figure 2.8 The typical shape for the thermal calibration in air. The calibration curve includes

the Peltier temperature and the probe voltage both plotted against time. .......... 27

Figure 3.1 A photograph of SThM set up at the University of York. Including the data logger,

probe power supply, Peltier power supply and detection circuit, the vacuum

facility and the AFM. The AFM control PC is the main control for the AFM. 30

Figure 3.2 a) A comparison between the thermal probe holder (left) and the contact probe

holder (right). b) A photograph of the thermal probe connector with a thermal

probe attached. ................................................................................................... 31

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Figure 3.3 A circuit diagram of the power supply of the probe. The probe is represented as a

variable resistor as each probe will have a variation in resistance. The arrow

showed the two variable resistors that controls the main voltage applying to the

tip and the fine adjustment to the voltage, labelled in the diagram. [34] .......... 32

Figure 3.4 The AFM feedback module panel showing the cable connection and the switch for

feeding the thermal signal into the AFM. .......................................................... 33

Figure 3.5 An SEM image illustrating a) the width and the length measurements from top

view, b) thickness measurements from the side view. ....................................... 36

Figure 3.6 The estimation of the tip apex of a) the thermal probe and b) the contact probe.

............................................................................................................................ 37

Figure 3.7 The figure of the sample arrangement on the heater. .......................................... 38

Figure 3.8 A schematic diagram showing the measurements made in a force curve. The

difference of Vmin and V0 is the adhesive force dF being measured. The line of

best fit for sensitivity measurements is noted. ................................................... 45

Figure 3.9 A typical result from the data logger for thermal calibration. ............................. 48

Figure 3.10 Figure of thermal calibration in vacuum heated at 60℃, the temperature jump

during cooling is marked. .................................................................................. 49

Figure 3.11 A typical measurement of probe voltage against Peltier temperature, a line is

fitted for estimating the conversion coefficient from voltage to temperature. .. 50

Figure 3.12 Illustration showing a close up of a thermal hysteresis with explanation of how

to measure the change in temperature. .............................................................. 52

Figure 4.1 shows the SEM image for all probes used in this project. Figure a)-c) are the

thermal probes A-C and d) is the contact probe D, the figures above were

measured with the scale bar of 10 μm. .............................................................. 55

Figure 4.2 The impurities on the cantilever of probe A, the impurity is located towards the

holder on the left-hand side of the picture. This could potentially affect the spring

constant estimation. ........................................................................................... 57

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Figure 4.3 The SEM image of probe B with layer of palladium resistor coating peeling off

after measuring a set of thermal measurement. The scale bar of the figure is

100nm. ............................................................................................................... 59

Figure 4.4 Silicon carbide topography measured with a) contact probe and b) measured with

thermal probe C. The figures represent a similar area of the silicon carbide. ... 60

Figure 4.5. Roughness analysis of gold thin film. ................................................................ 63

Figure 4.6. Roughness analysis of mica. .............................................................................. 63

Figure 4.7. Roughness analysis of PTFE. ............................................................................. 64

Figure 4.8. Roughness analysis of silicon. ........................................................................... 64

Figure 4.9. Roughness analysis of silicon carbide. ............................................................... 65

Figure 4.10 Force measurement results of silicon carbide measured in air with a) the contact

probe D and b) the thermal probe C. ................................................................. 69

Figure 4.11 A diagram illustrating the force measurements that exceeded the AFM limit. Two

gradients were drawn and the intercepts were used to determining the adhesive

force. .................................................................................................................. 70

Figure 4.12. A diagram showing the typical force measurement result of silicon after the offset

of sensor limit. ................................................................................................... 71

Figure 4.13 Force result of PTFE in vacuum, measured in three different areas showing the

variation. ............................................................................................................ 74

Figure 5.1 a) A generic result of data logger recording in air. The diagram illustrates each part

of the curve during the experiment. From the beginning there is a potential

difference drop for approach until the tip is in contact with the surface. Then the

potential difference remained during the topography scanning. b) Continue the

same diagram with labels of the measurement spikes, noise spikes and indication

of the data logger change in temperature. The measurement spikes are indicating

the temperature changes during the force and thermal measurements. The noise

spikes are caused by the 40-second periodic instrumental noise. The data logger

change in temperature indicates the temperature difference between the tip in

contact and out of contact of the sample. .......................................................... 79

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Figure 5.2 Data logger results of mica with 0.8mA in the environment of a) in air and b) in

vacuum. The results are comparing the measurement spikes height to the

temperature when the tip is not in contact in both environments. .................... 81

Figure 5.3 The data logger results of thermal calibration with the probe current of 0.8mA a)

in air and b) in vacuum. ..................................................................................... 83

Figure 5.4 Results of thermal calibration, graph of probe voltage against Peltier temperature

measured in a) air and b) vacuum. ..................................................................... 84

Figure 5.5 A graph of thermal calibration peak with both heating and cooling. .................. 85

Figure 5.6 a) The unprocessed thermal map of SiC in air b) the processed thermal map of SiC

in air. For both figures the conversion 10.02pm/V. ........................................... 87

Figure 5.7 Thermal curve of PTFE measured in vacuum. The thermal curve presented is an

average of 9 curves. The step jump is caused by different responses at each area.

............................................................................................................................ 89

Figure 5.8 Thermal curve of PTFE at 3 different areas measured in vacuum. ..................... 90

Figure 5.9 The thermal curves of a) PTFE and b) SiC measured in air. .............................. 91

Figure 5.10 The results for gold thin film in air. .................................................................. 93

Figure 5.11 Thermal results of Mica in air. .......................................................................... 93

Figure 5.12 Thermal results of PTFE in air. ......................................................................... 94

Figure 5.13 Thermal results of Silicon in air. ....................................................................... 94

Figure 5.14 The results of silicon carbide in air. .................................................................. 95

Figure 5.15 Thermal results of thin film gold in vacuum. .................................................... 99

Figure 5.16 Thermal results of Mica in vacuum. ............................................................... 100

Figure 5.17 Thermal results of PTFE in vacuum. .............................................................. 100

Figure 5.18 Thermal results of silicon in vacuum. ............................................................. 101

Figure 5.19 Thermal results of silicon carbide in vacuum. ................................................ 101

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Figure 5.20 The data logger results of silicon in air showing the sample cooling during the

experiment. ...................................................................................................... 107

Figure 5.21 Result of PTFE illustrating the method of calculating deformation temperature

changes. ........................................................................................................... 110

Figure 5.22 The approach temperature change against the thermal conductivity. ............. 112

Figure 5.23 The approach temperature change against the thermal conductivity for small

thermal conductivity. The gold is shown as a horizontal line as the thermal

conductivity is not known. ............................................................................... 113

Figure 5.24 The approach temperature change against the thermal conductivity for small

thermal conductivity. The silicon values have plotted with the silicon oxide

thermal conductivity of 1.1 W/m⋅K. ................................................................ 114

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Acknowledgement

I would like to take this chance to thank my supervisors, Prof. Sarah Thompson and Dr. Siew

Wai Poon for the unlimited encouragement, patience and care in this project. Without their

excellent guidance, I probably would never complete this research.

I want to thank my parents for looking after me throughout the time I have been writing, their

constant support and belief has helped me to pass through difficult times.

I want to thank a couple of my friends, Gordon Kam, Lichi Sun and Winky Wong for the

spiritual support.

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Declaration

I declare that this thesis is a presentation of original work and I am the sole author. This work

has not previously been presented for an award at this, or any other, University. All sources

are acknowledged as References.

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Chapter 1 Introduction

1.1 Motivation and introduction

Classical thermal measurements have been developed for understanding thermal physics for

decades. The classical theories of thermal transportation have been developed for investigating

the thermal properties of materials such as thermal conductivity and the applications have been

widely applied across everyday life. There are many techniques for making thermal

measurements, for example the absolute technique method determines the thermal conductivity

by placing the sample between the heat sink and a heat source, calculating the length of the

heat flow through the sample and obtaining the thermal conductivity by Fourier’s law. [1]

There are other temperature sensors that use different mechanisms such as thermocouples and

resistance thermometers.

When quantum physics was developed the technology and theories advanced further. There

was a better understanding that thermal transport is different on a smaller length scale, for

example the concept of heat carriers was introduced. [2] When making thermal measurements

at a nanoscale, typically less than 100 nanometres [2], a different mechanism of thermal

transportation would be expected. With the advance of fabrication technology, the construction

of materials and electronic components became much smaller. Although classical methods

such as the 3ω method [1] have advanced for thin film materials, the classical methods still

require a large contact area. Non- contact methods for thermal conductivity, such as transient

thermoreflectance techniques measure the thermoreflectance response of the material as a

function of time using a laser and beam splitter [1]. The thermoreflectance method can detect

the thermal conductivity of thin film with a few nanometres thick, but the spatial resolution

with this method can only measure down to 400 nanometres due to the optical limit of

diffraction. [3] Thermal measurements at smaller scale require other techniques. The scanning

2

thermal microscope is capable of measuring the temperature at 10 nanometres [4], it is a

modification to an atomic force microscope, which leads to the introduction to atomic force

microscopy.

Binnig introduced Atomic Force Microscopy (AFM) in 1986 [5], it is a technique which allows

high spatial resolution measurements at the material surface. Later the AFM was modified to

measure various properties, particularly the scanning thermal microscopy that is used in this

thesis. The original AFM modified the scanning tunnelling microscope tip by sticking pieces

of diamond on the end of the cantilever [5], [6]. In modern AFM the tip is no longer diamond,

instead it is usually made of silicon and silicon nitride. [7] The AFM detects the Van der Waals

force on the tip [8], the key features of AFM will be discussed in Section 1.2. AFM can provide

images with spatial resolution better than 0.1 nm, with the advantage of using non-conductive

materials and can be operated in vacuum. AFM has been widely used in material science in

order to study the topographic, tribological, roughness and adhesion characteristics of materials.

[7]

Shortly after AFM was introduced, scientists made modifications for temperature

measurements [9], the modification took the advantage of the high spatial resolution scanning

ability of AFM. The first Scanning Thermal Microscopy (SThM) instrument was introduced

by Williams and Wickramasinghe in 1986 [9]. The principle of their SThM was similar to

AFM, modifying the tip into a thermocouple that allows thermal measurements. As the tip

makes contact with the sample surface, thermal energy transfers either from the sample to the

thermocouple or vice versa, which changes the temperature dependent voltage across the

thermocouple. The voltage measurement could be converted into temperature, along with the

topography, creating a thermal map. Various types of SThM tip have been developed since

using different types of mechanisms, for instance the thermoelectric effect and thermal

3

resistance. The details of the different types of probes will be discussed in Section 1.3. SThM

gives a high spatial resolution thermal image, which makes this technique unique in studying

thermal physics.

SThM now acts as one of the main tools for developing near field thermal physics and in

material science. This thesis will attempt to explore its potential for measuring the thermal

properties of materials at the nanoscale. The thesis will focus on the initial steps of developing

a quantitative method for making thermal and force measurements, the method is capable of

operating the SThM in both air and vacuum environment. Thermal and force measurements

were obtained with five different samples covering different thermal and mechanical properties.

The topography analysis, interpretation of force and thermal curves will be discussed.

The thesis will start by introducing the concept of AFM, the principle of how to make

measurements and what modes they can be operated in, then move onto SThM by describing

the different types of probes and the literature review on the application. Chapter 2 discusses

the physics of thermal transport and how the heat flows in SThM. This then leads to the

discussion on how to interpret the force and thermal measurements. Chapter 3 describes in

detail the instruments being used in this thesis, the experimental setup and process and the

choice of samples. Chapter 4 concentrates on the analysis of the force measurements while

Chapter 5 concentrates on the analysis of the thermal measurements. Chapter 6 is the

conclusion and suggestions for future development.

4

1.2 Atomic Force Microscopy

AFM systems operate on a vibration isolated platform, as AFM is measuring in high spatial

resolution, any form of vibration could result in a large error in measuring the topography. A

generic AFM features the following main parts: probe, piezoelectric tube to scan the sample,

laser detector to measure the flexing of the cantilever, feedback controls and the computer

control. A generic structure of an AFM is shown in Figure 1.1.

Figure 1.1 A generic diagram of the main parts of an atomic force microscope, it consists of a

piezoelectric tube as the main driver of the specimen, a laser and a photodiode for feedback system a

cantilever for scanning. [10]

In figure 1.1, the piezoelectric tube is placed beneath the sample. The piezoelectric materials,

used as the main drivers in AFM are materials that expand or contract when an electrical

potential is placed across them. They are usually ceramic materials with a typical expansion

coefficient of 0.1nm per applied volt. [7] The piezotube is placed under the specimen stage to

control the x-y direction of the sample. The piezotube to control the z direction is placed under

the x-y piezotube that gives an independent control over z direction. The reason for that is the

5

z-piezotube is combined with a feedback circuit that requires an independent control. In some

types of AFM, the z piezotube is placed on the cantilever holder.

A laser beam is set to reflect off the back of the cantilever to a photo diode that locates the tip

in the z direction and the photodiode is connected to the feedback control circuit. When there

is a force pulling the tip towards the surface it causes a bend in cantilever. The reflected laser

beam position on the quadrant photodiode therefore changes, and this signal would be sent to

the feedback circuit. The feedback circuit can then send a signal to the z piezotube to move the

sample away from the tip so as to maintain the probe sample distance if desired. This

mechanism works vice versa when there is a force pushing the tip away. The feedback

mechanism can minimise the damage from an uneven surface, this is because the laser is

reflecting the status of the cantilever when the tip feels a change in force. This method increased

the sensitivity compare to a tradition stylus profiler. [7]

As the AFM detects the electrical signal from the photodiode to make changes and for force

measurements, it is necessary to know the cantilever spring constant in order to convert the

voltage signal back in units of nano-Newton if the force is needed to be known. AFM probes

were then later developed to measure the magnetic properties in magnetic force microscopy,

and to measure thermal properties in scanning thermal microscopy.

The AFM can be operated in two main modes, contact mode and non-contact mode. In contact

scanning mode, the probe is in contact with the sample surface and a small force is applied

from the cantilever to the surface to make it in contact. As the contact area of the probe is small,

the force pressing on the sample must be small in order to prevent scratching of the sample

surface or to the tip. [11] To measure the topography, the height of the probe is kept constant

such that as the probe scans across the surface, the Van der Waals force will repel the tip

according the height of the structure. This leads to a bend of the cantilever and changes the

6

laser reflection. The photodiode gives a signal to the computer for the z geometry measurement

at each point. This method is often referred to as constant height scanning mode.

Constant force scanning mode is to maintain the force at a fixed value between the probe and

the surface. This technique is similar to constant height scanning mode, except the deflection

of the cantilever signal from the photodiode is sent to a feedback circuit. The feedback circuit

controls the z piezotube to adjust the height of the probe such that the force between the probe

and sample surface is maintained. Although both the contact scanning modes can provide

topography images, there are some defects and limitations. For example, the force on the

surface could cause friction and bend the probe, the probe could cause damage while moving

on the surface. Due to these limitations, non-contact scanning mode was introduced.

Non-contact scanning mode is a technique which uses the resonance effect of the cantilever.

Unlike the contact force mode, the tip does not constantly contact with the sample surface,

instead the cantilever is oscillating using an additional piezoelectric element. The cantilever is

oscillating at its resonant frequency, when the probe approach to the sample surface, the

cantilever is no longer oscillating in free space. A phase shift is then detected in the resonant

frequency of the cantilever because of the interaction force between the tip and the surface. [7]

From this phase shift, we can determine whether the surface force is attractive or repulsive.

The feedback circuit then sends a signal to adjust the z position in order to maintain the resonant

frequency. [7] [8] While the tip moves across the x-y plane, along with the change in z position,

the surface topography is then generated.

7

1.3 Scanning Thermal Microscopy

The general principle for SThM making thermal measurements is to use a tip with a physical

property that is sensitive to temperature and can be monitored continuously. [12] This property

is usually electrical potential. A constant electrical current is first passed through the fabricated

material at the end of the tip, where the thermal sensor for detecting temperature is located.

When the probe makes contact with the sample surface, the heat flow causes a change in

temperature at the tip, this changes the electrical potential detected across the tip sensor. By

monitoring the value of the voltage changes simultaneously with the topography, a thermal

map is produced. SThM is usually carried out using the contact mode of AFM. The reason is

the thermal measurements are related to the changes of voltage when the tip is in contact with

the sample, a continuous contact with the sample is preferred for SThM.

a) b)

Figure 1.2 a) A conventional AFM topography image of a gold sample along with b) the associated

thermal image. The conversion coefficient for the scale bar to voltage is 2.34Å/V.

Figure 1.2 shows a typical result from SThM, it is usually a topography map along with a

thermal image. The pictures show that the thermal image provides some fine details to the

topography, which could suggest the change in tip temperature could help in determining the

surface structure. During the measurement, the tip and the sample could cause a misleading

representation. This is because the contact area between the tip and the sample is dependent on

200nm

45.75 nm

0.00 nm

200nm

2.70 Å

0.00 Å

8

the physical properties of the sample surface and the thermal transport depends on the contact

area, if the contact area changes, the thermal transport changes. [13]

There are several types of SThM probes that have been developed for measuring surface

temperature, each can be classified using its temperature-dependent mechanism. [12] This

thesis will mainly discuss the types of probe using the mechanisms of thermal voltage and

change in electrical resistance; other thermal probes for example fluorescence and thermal

expansion are not covered in this thesis.

A thermocouple profiler is one of the popular probes being used in SThM, where the

temperature is measured by the change in electrical potential at the thermal junction. The

thermocouple profiler was first developed by fabricating two types of materials to form a

thermocouple at the end of an STM tip, the coating is typically about 100nm thick. [8] This

type of probe uses the concept of thermoelectric effect, which offers a direct conversion

between electrical voltage and temperature. [14] Thermocouple probes measure the voltage at

the junction that is in contact with the sample surface and give a spatially resolved temperature

measurement.

A resistance thermometer is another type of probe which monitors the temperature changes

using a voltage measurement. The change in temperature is monitored by applying a constant

current through the sensor. When the temperature of the probe changes, this causes a change

in the electrical resistance of the sensor, which in turn causes a change in electrical potential

across the tip. There is only one type of material fabricated on the AFM tip, therefore the

technology required for making resistance thermometer is less complex [15].

Wollaston wire tips are one of the probes that measured the temperature by the change in

resistance, introduced in 1994 by Pylkki et al. [16] The tip is made by bending a Pt wire, 5 μm-

9

core, into a V-shape and the rest of the wire forms a cantilever. The cantilever is coated with

thick Ag of about 75μm in diameter. A mirror is then stacked on the back of the cantilever

across the wires to provide reflection for AFM signalling and the end of the cantilever is

mounted on a ceramic insulator. The Wollaston wire is responsive to temperature changes

through its temperature dependence of resistance and has a high temperature coefficient of

0.0017 𝐾−1 [12], however its large contact area of about 1 μm [17] limits the thermal research

ability at smaller scale.

Figure 1.3 a) A typical shape of a fabricated probe. b) shows the structure of a Wollaston wire. [18]

A fabricated resistor probe is another type of probe that has improved the spatial resolution

beyond that of a Wollaston wire. The cantilever is made of silicon nitride, with a thin palladium

resistor fabricated at the end of the tip [14]. The fabricated resistor probes that will be used in

this thesis are designed by Dobson et al. [15] in Glasgow, where the probes are produced by a

batch fabrication process. The shape of the cantilever is formed through several processes of

photolithography and micromachining, then the palladium resistor and the gold connectors are

fabricated at the end of the tip. [15] The fabricated probe provides a contact area of radius about

50 nm, which is much smaller than the Wollaston wire. [12] Figure 1.3 shows the size

difference between the Wollaston Wire and a fabricated probe.

10

SThM requires extra components to modify an AFM to measure the surface temperature of the

sample, this is usually specific to the type of probes that the SThM is using and the capability

of the AFM. In general, from the probes mentioned above, it is required to constantly monitor

the small change in current through the probe by measuring the voltage across it. This means

that the AFM probe holder must be modified for electrical connections. An additional power

supply is required for providing the current through the probe. A signal recorder which can

feed the signal back to the AFM for monitoring the voltage is also required. The details of the

apparatus modification will be discussed in Chapter 3.

SThM can be operated in active and passive modes. Active mode is to pass a current through

the probe to monitor the change in temperature, with no additional heating of the sample. The

sample is heated up only by the tip, as the current in the probe causes Joule heating. This defines

the direction of heat flowing from the tip towards the sample [19]. Passive mode is opposite to

active mode, where the sample is heated independently by a heater. The current passing through

the tip is smaller and only acts as thermometry, the sample heating being large enough to

overcome the Joule heating by the probe. In this mode therefore, the heat flow is from the

sample towards the probe. The advantage of active mode is that the mechanism of thermal

transport is simpler than passive mode and the heat generation is localised to the tip area.

Research on nanothermal analysis using SThM has been actively developing in recent years.

Majumdar and Shi [13] investigated the heat transfer mechanisms at SThM, which defined the

main thermal transport paths at the tip-sample contact. Weaver et al. [20] developed methods

of mass producing thermal resistive probes as well as designing different configurations. For

example, they suggested there is a strong thermal coupling through air between the tips in dual

cantilever probes. Gomes [17] studied the thermal exchange between probe and the sample, the

result suggested that the environment where the SThM performs affects the heat transport.

11

Prater et al. [21] have reported using infrared AFM on nanoscale infrared spectroscopy, which

could potentially open up nano thermal microscopy for biological use. Robinson et al. [22]

reports the investigation of how shear force affects the contact area of heat transport on the

nanoscale and proposed that the shear force at the thermal junction was dependent on the

materials. Gorbunov et al. [11] measured the surface microthermal properties of low thermal

conductivity materials and reported that local deformation contributes to the thermal

measurements.

The SThM at the University of York has the unusual ability to undertake thermal measurements

in vacuum. The advantage for vacuum is being able to eliminate the gas heating effect between

the probe and the sample, the details of this will be discussed in chapter 2. High vacuum SThM

is starting to get popular for nanothermal analysis. Menges et al. [23] built a high vacuum

SThM at the IBM research laboratory for the research on thermometry at nanoscale. Kim et al.

[24] reported using high vacuum SThM to quantify thermal fields in nanowires during

electromigration.

12

1.4 Objectives of this project

The objective for this project is to explore the potential of using a scanning thermal microscope

for quantitative thermal transport measurement. The scanning thermal microscope used in this

project is based on the atomic force microscope at the University of York. The thesis will start

by introducing the operation of the AFM, then move onto the development of the modification

to SThM. The unusual property of the SThM at York is the ability to undertake thermal

measurements in vacuum. As the SThM at York is still under development, this project aims

to develop an experimental procedure for quantitative measurements in different environments.

Then the project will move onto exploring the topography and the surface features of the

sample. The tip temperature changes will be measured using the SThM and compared within

the set of five different samples that cover different thermal and mechanical properties: silicon, silicon

carbide, mica and PTFE along with a thin film of gold for which the thermal conductivity would be

determined. An attempt to explore the connection between the adhesive force and the

temperature measurement will be presented as well as an attempt to obtain the thermal

conductivity of a thin film sample, and compare this to the bulk value. The project will conclude

with further suggestions on how to improve the experimental procedure and further possible

research directions.

13

Chapter 2 Principle of force and temperature measurements using

scanning probes

This chapter will include the basic theory of SThM. The chapter will start with discussing the

heat transport in SThM followed by the theory behind force curves and methods for measuring

the spring constant of the cantilever. The chapter will conclude with explaining the thermal

measurements, from the heat transport point of view, the complementarity with force

measurements and the thermal calibration.

2.1 Heat Transport in SThM

In SThM, the thermal properties are investigated by mapping the thermal properties to the

topography of a sample. It is important to understand how the thermal energy flows in the

system and what factors could limit the heat flow. There are four main mechanisms of thermal

transport in SThM, Figure 2.1 illustrates the heat flow from a hot tip into a cold sample.

a) b)

Figure 2.1 A schematic diagram showing the thermal pathways of a probe in contact with a sample. a)

This diagram shows the SThM operating in ambient environment. The setup is the probe when operating

in active mode. The heat flow is directed from the probe to the sample. The heat transport by air, 𝐺𝑔𝑎𝑠

is also shown in the diagram. Note that 𝐺𝑔𝑎𝑠 does not exist when the setup is operating in vacuum. b)

A detailed diagram of the dotted circle area in figure 2.1a), showing the heat flow paths from the tip to

the sample. In both the environments, the heat transported by the radiation 𝐺𝑟𝑎𝑑 and by mechanical

contact 𝐺𝑚𝑐 exist. The blue area in the ambient environment represents the water droplets formed by

condensation. The heat transport via water is represented by 𝐺𝑤. Note that 𝐺𝑤 does not exist in vacuum.

The diagrams are modified from Poon [25] presentation.

𝐺𝑔𝑎𝑠 𝐺𝑟𝑎𝑑

𝐺𝑤

𝐺𝑚𝑐

𝐺𝑤

𝐺𝑟𝑎𝑑

𝐺𝑚𝑐

14

Figure 2.1a shows a setup of a probe contacting a sample surface, where the probe is heated to

have a higher temperature than the sample. Figure 2.1b shows the thermal energy transfer in

the environment of ambient and vacuum. The four main heat transport mechanisms are shown

and represented by their thermal conductance. The Grad, Ggas, Gw, Gmc, represent heat transport

by radiation, gas conduction, solid-liquid conduction and mechanical conduction respectively.

Gth,c represents the effective thermal conductance of the overall system. The mathematical

representation of Gth,c is proposed by Shi and Majumdar [12] in equation (1)

Rth,c =1

Gth,c=

1

Grad+Ggas+Gw+Gmc (1)

Equation (1) shows that the effective thermal resistance Rth,c , the reciprocal of effective

thermal conductance, Gth,c, which is the sum of the thermal conductance of all mechanisms.

Mechanical, or solid-solid conduction, is a direct energy exchange between the probe and the

sample [8]. The conduction happens when both the probe and the sample are in contact,

therefore during the thermal measurements the direct conduction must be taken into account.

The solid-solid conduction is restricted by the contact area between the tip and the sample, this

can be demonstrated by Fourier’s law of heat in equation (2).

Q̇ = −kAdT

dx (2)

Where Q̇ is the local heat flux, k is the thermal conductivity of the material, A is the area of

conduction, dT is the change in the temperature of two points and dx is the distance between

the point of measurements. When applying equation (2) in SThM, A is the contact area between

the probe and the sample surface. Fourier’s law shows that Q̇ is directly proportional to A,

15

therefore if the contact area of the tip gets infinitely small, the heat transport via conduction

will be infinitely small.

Fourier’s law described the thermal transport system on a macroscopic scale, the properties of

the materials such as the surface structure were not taken into account. In the microscopic

viewpoint, thermal transport is described using the concept of heat carriers. [2] Heat carriers

are carriers that transport energy, resulting in the change in temperature, for example, photons

are the main heat carriers of thermal radiation. [2] Heat carriers can be determined by quantum

mechanics with different possible energy states. In a solid, energy transfer can also be described

using phonon vibration.

Gas conduction happens when the heat transport is via gas molecules in the surrounding air.

Classical treatment of the kinetic theory of gases shows the thermal conductivity of the gas is.

[8]

kg =1

3Cvl (3)

Where kg represents thermal conductivity of the gas, C is the heat capacity per unit volume, l

is the mean free path for intermolecular collision and v is the root mean speed of the molecules.

When the tip heats up far away from the sample, thermal energy will disperse into the air and

heat up the surrounding gas molecules. The hot air molecules move away and convection

occurs. When the tip reaches the sample, the tip-sample distance gets smaller than the mean

free path of the air, the air would then transport heat energy directly and act as a conductor [26],

[27].

16

Thermal radiation happens when SThM is operating in both ambient conditions and in vacuum.

It is possible to model the far field radiation from a classical point of view using the Stefan-

Boltzmann law by assuming the system acts as a black body.

Q̇rad = σA(Thot4 − Tcold

4) (4)

Where Q̇rad is the power emitted by the black body radiation, Thot and Tcold represent the

temperature at the heated end and the cold end, A is the emitting area and σ is the Stefan-

Boltzmann constant, 5.67 × 10−8 kg s−3 K−4. Assuming the emitting area is the end of the tip,

A is very small. As there is a direct relationship between A and Q̇rad, the power emitted will

also be very small due to the geometry of the probe. Wien’s displacement law models the peak

wavelength of the black body by the following equation.

λmax =b

T (5)

Where λmax is the peak wavelength, T is the absolute temperature and b is the Wien’s

displacement constant, 2.898 × 10−3 m ⋅ K. Assuming the typical room temperature is about

300K, when applying to equation (5), the λmax is approximated to 10 μm. The typical size of a

thermal probe is less than 10 μm, therefore the classical theory could not be valid on measuring

thermal transport smaller than this scale. The above classical theory shows that near field

radiation theory is necessary to model heat loss via radiation. It is experimentally challenging

to measure the heat loss due to radiation, this is because the thermal radiation does not play the

main role in nano-thermal transport. [8] In an example of the thermal experiment done in

vacuum, the main transportation methods are solid-solid conduction and thermal radiation.

When the tip is not in contact with the sample, the signal is almost unchanged as the tip was

moved further away.

17

Solid-liquid conduction occurs when the ambient humidity is not zero and a water meniscus

forms on the tip due to condensation. The water meniscus increases the contact area between

the tip and the sample as illustrated in Figure 2.1 shown earlier. The heat energy takes the path

through the water then to the sample. Since the water is acting as a conductor, it is possible to

model the thermal energy with Fourier’s law. Luo et al. [26] suggested a model based on the

Kelvin equation. It is possible to eliminate solid-liquid conduction by performing SThM

measurements in vacuum.

18

2.2 Characteristics of a force curve measured by AFM

Material properties such as hardness and roughness of a surface have effects on thermal transfer

between a thermal probe and surface. For example, for a given contact force, a softer surface

is expected to have a larger contact area with the thermal probe which will contribute to the

solid-solid heat transfer. Fortunately, these properties can be studied using force curve

measurements provided by AFM. This section will provide a detail analysis for measuring the

adhesive force of the sample using the AFM force curves.

In imaging mode, AFM system provides a feedback circuit to maintain a constant contact force

between the tip and the sample. In a force curve measurement, which is done on a fixed surface

position, the contact force is varied by systematic movement of the AFM piezoelectric towards

and away from the sample position. The deflection of the probe cantilever due to this force

variation is recorded simultaneously. An analogous thermal curve can also be recorded on this

sample position when the AFM records the probe thermal voltage instead of cantilever

deflection. Descriptions on thermal curves will be provided in the next section.

A topography scan is required for the SThM to make a force measurement. It should be done

on a smooth area of the sample to avoid any impurities that could affect the adhesive force.

The smoothness of the sample is analysed by measuring the local roughness. A point on the

surface will then be selected by the user to take the force curve measurement. Usually several

points will be selected. The importance of roughness for thermal measurements will be

discussed later.

In a force curve measurement, the tip will first be retracted vertically away from the surface to

a selected start position shown in Figure 2.2. The laser position on the photodiode reflected

from this interaction-free cantilever at rest is taken as the reference voltage, V0. The AFM

piezoelectric will then start moving the tip towards the surface (known as tip approach) until a

19

contact is made. This position is labelled as ‘contact point’ position in Fig. 2.2. At this position,

the adhesive and capillary forces of the surface prematurely pull the tip towards the surface and

cause the cantilever to bend. The bending causes the laser reflected from the cantilever to move

to a position different from V0. The tip would carry on pressing into the sample which makes

the cantilever bends further in the opposite direction until a pre-set displacement range is

reached.

Figure 2.2. A typical force measurement diagram of SiC sample and operated in air. The diagram

describes the probe position at each point from the starting position where the probe starts recording

the data, approaching to contact point where the probe makes contact with the sample surface. The tip

keeps pressing on until the tip stop at the pre-set displacement range labelled as tip stopping point. The

tip will then retract from the surface, the surface adhesive force is keeping the tip on the surface and

bending the cantilever, a hysteresis is formed during the tip is retracting. When the tip gained enough

force that overcomes the surface force, the tip will snap out and retract to the starting position.

After the tip stopped, the piezoelectric will move in the opposite direction and the probe starts

its retraction from the surface. It is noted that the deflection path of retraction does not exactly

follow the approach path. The reason is the voltage and displacement of the piezoelectric are

nonlinearly related. [28] This results a curved path of deflection, which would affect the

20

sensitivity measurement shows in figure 2.3. When the tip reaches the contact point again, the

adhesive force from the sample keeps the tip in contact with the surface, i.e. the tip “sticks” on

the surface. This causes the cantilever to bend until it reaches a point where there is enough

force to overcome the adhesive force. The tip will then snap out of the surface and returns to

the reference point at V0.

In the retract direction, the extra adhesive force provided by the cantilever-tip interaction

causes a hysteresis, this extra force in retraction is where the adhesive force is measured. The

point taken for this force is the difference between minimum point before snapping out and at

V0.

The figure 2.2 shows the force curve with a single layer of bulk material, the force curve is

expected to be different when there is an extra surface layer on the surface for example water

or oxidized material.

The AFM system collects the force signals in voltage. Therefore, the raw signal needs to be

converted to force in Newton units. In order to convert this voltage into a force in nano-

Newtons, the spring constant of the probe needs to be known. The conversion can then be done

using Hooke’s Law as follows:

F = κα(V − V0) (6)

α =|d2|−|d1|

V2−V1 (7)

Where F is the force measured in nN, κ is the spring constant of the cantilever, measured in

N/m. V is the potential measured at each point on the force-displacement curve, V0 is the

reference potential, both the potentials are measured in volt. α is the optical lever sensitivity,

which is a measure of the change in displacement d divided by the change in potential V during

retraction. This is represented in equation (7), where d1, d2 are the distance of the vertical

21

direction of the tip moving, measured in nanometres, and V1, V2 are the electrical potential that

is recorded in AFM, measured in V. Figure 2.3 illustrates where the measurements should be

taken on a generic force curve.

Figure2.3. Schematic diagram of force displacement curve. 𝑉0 is the reference voltage when the tip is

away from the surface and the sample is exerting no force on it. The optical lever sensitivity 𝛼 is

measured at the retract regime, note that the sensitivity is the inverse of the gradient at the retract curve.

[29]

Recalling the figure 2.2, the deflection path during retraction has shown to be a curve due to

the nonlinear piezoelectric, which is different from figure 2.3. The measurements described in

figure 2.3 should use the linear range of the retract deflection when analysing the sensitivity.

There are a few methods for cantilever spring constant measurement. The most common way

to measure the spring constant is the dimensional method. This method is developed using the

material properties combined with Hooke’s Law, assuming the cantilever to be rectangular.

F = −κx (8)

E =Fx0

A0x (9)

In the spring case, the Hooke’s Law in equation (8) is used to describe the relationship of spring

constant and the force, where F is the applied force, κ is the spring constant, x is the

displacement of a spring. Equation (9) shows the method for obtaining Young’s modulus, E.

22

A0 is the cross-sectional area of the spring and x0 is the original length of the spring. The

cantilever spring constant was reported by Poggi et al. [30] using the following equation.

κ =Ewt3

4L3 (10)

The notations for equation (10) are the same as in equation (8) - (9), where κ is the spring

constant, E is the Young’s modulus, w is the width of the cantilever, t is the thickness and L is

the length of the cantilever.

In 1993, Cleveland [31] proposed a method of measuring the spring constant of the AFM

cantilever by adding a known mass at the end of cantilever. The principle relies on measuring

the natural frequency of the cantilever before and after adding the known mass, from the

difference of the frequency to obtain the spring constant. As the natural frequency measurement

is independent of the shape of the probe, this method can measure the spring constant with a

more complex cantilever design.

However, as the probe structures are getting more complex with more than one material

involved, it is difficult to measure the Young’s modulus. Sader et al. [32] published a method

to measure the spring constant with an arbitrary shaped probe based on his previous method,

which opened up more possibilities for probe designs and choice of materials. The Sader

method is based on Cleveland method, but instead of adding a physical known mass to the

cantilever, Sader measured the resonance frequency of the AFM cantilever in air and in vacuum.

This method has an advantage that it is not restricted to shape or the material of the cantilever.

κ = MeρctwLωvac2 (11)

Where κ is the spring constant, ωvac is the fundamental radial resonant frequency of the

cantilever in vacuum; t, w and L are thickness, width and length of the cantilever respectively,

23

ρcis the density of cantilever and Me is the normalized effective mass. The advantage of this

method is that the shape of the cantilever is not restricted, this is because the spring constant is

heavily relying on the quality factor when measuring resonant frequency in vacuum. However,

this method requires the density of the cantilever, as the structure of SThM tip becomes more

complicated with more materials, it is challenging to estimate the density of the cantilever.

Figure 2.4 A schematic diagram demonstrating the reference cantilever method using a large-scale

cantilever against the AFM cantilever. a) The AFM cantilever is pressed on a large-scale cantilever

that has known property. b) When a force is applied by the AFM cantilever, both cantilevers will bend

as different rate, since both cantilevers are exerting the same force, the spring constant is measured by

the deflection of the cantilever. [33]

The referencing cantilever method is a more recently developed method, the principle is uses

a larger scale cantilever with known spring constant to calibrate the spring constant. Figure 2.4

demonstrates the reference cantilever method. The AFM probe is pressed against a larger scale

cantilever, both cantilever would then bend at different rates. Since the force applied to each

other are balanced, with the known large-scale cantilever spring constant, we can then work

out the spring constant using Hooke’s law. [33]

The dimensional method to estimate the spring constant will be used in this project. The reason

is due to the simplicity of the procedure as this project is aiming to develop a method for

exploring the thermal properties of the material. For this project, a scanning electron

microscope will be used for measuring the dimension of the probe.

24

2.3 Characteristic of a thermal measurement and thermal calibration

In section 2.2, the cantilever bending was described along with the force measurement. The

thermal curve follows a similar principle; however, the input channel is used to measure the

voltage corresponding to the temperature. Figure 2.5 shows a generic thermal measurement

measured in air.

Figure 2.5 A schematic thermal measurement of SiC in air using a fabricated resistor probe in active

mode. The arrows indicate the motion and position of the probe throughout the measurement. The

position at which the probe snaps into the surface is marked as the contact point.

The tip is first retracted from the sample surface to the pre-set displacement position, labelled

starting position in figure 2.5, and then starts to approach the surface. The temperature will

start dropping due to air conduction increasing as the tip-sample distance gets smaller. When

the tip gets closer to the sample surface, the tip snaps into the sample surface at the contact

point, this is the same as described in the force measurements. The temperature signal will have

a sudden sharp drop, this is because the solid-solid conduction and solid-liquid conduction

happens and there is suddenly more heat flowing through the interface.

The tip will then continue pressing into the surface as the z-motion continues. The sample

surface will deform if the sample is soft or the tip will deform if the sampler is harder than the

25

tip. If either of these happen, then this will increase the contact area between the probe and the

sample surface and increase the amount of solid-solid conduction therefore cooling the probe

further. The tip will stop at the pre-set displacement and start retracting from the surface. When

the cantilever retracts, from the force measurements we know that the tip will remain in contact

until the cantilever has enough force to overcome the adhesive force, the tip temperature

remains largely the same during this process. Then when the tip snaps out, the temperature of

the probe increases back to the temperature before it approached.

Figure 2.6 A typical thermal result of SiC measured in vacuum operated in active mode. The main

characteristic is there is no heat loss before the tip reaches the contact point.

Figure 2.6 shows a thermal curve measured in vacuum. Here, the temperature at the starting

position is similar to the temperature at the contact point, until the tip snaps into the sample,

unlike in figure 2.5 where there is a temperature drop from the starting position to the contact

point. This is because in vacuum the air conduction and solid-liquid effects are eliminated,

there were no air or water molecules disposing heat from the tip. [13] The thermal transport

paths in vacuum have reduced to only solid-solid conduction and thermal radiation, the

temperature drop in vacuum will be reduced by this smaller contact area with no meniscus.

26

The force measurement is also used in verifying where the temperature drops. When putting

the force curve and the thermal curve together, the intersection of the curves shows the

geometric point where the probe is in contact and out of contact with the sample. This is shown

in Figure 2.7.

Figure 2.7 A force curve and a thermal curve to verify the interpretation of the thermal curve. The

intersection of both curves at the contact point and the snap out point are used to verify the temperature

change on the thermal curve.

Figure 2.7 shows the direct comparison of both force and thermal curves placed on the same

axis. Recalling the figures 2.2 and 2.5, the probe position at each point was described

individually from the force and thermal result. However, both force and thermal measurements

are measured through the same instrument at the same point, the probe movement should be

identical between figure 2.2 and figure 2.5.

The change in temperature would require a conversion for the voltage signal back into ℃ for

comparison. The calibration process involves heating up the tip with a heater to a known

temperature. When the tip reaches the preset temperature, the heater is turned off and the tip

left to cool naturally. This results in a graph of temperature against time for the heater and a

27

graph of voltage against time for the tip. Figure 2.8 demonstrates the temperature recorded for

the Peltier heater and the probe.

Figure 2.8 The typical shape for the thermal calibration in air. The calibration curve includes the

Peltier temperature and the probe voltage both plotted against time.

Although in chapter 2.1 the different heat transport mechanisms were described, for the

calibration, the tip and the heater are in contact during heating. After a certain amount of time

the tip and the heater are in thermal equilibrium. The temperature of the heater should therefore

be proportional to the total temperature detected by the tip. This is shown in equations (12) -

(13)

Tpeltier ∝ Vtip (12)

Tpeltier = B Vtip (13)

The Tpeltier is the temperature of Peltier, Vtip is the recorded voltage of the tip, B is the

conversion factor for converting temperature and the voltage. The conversion should use the

values that were recorded when the probe is cooling. The conversion coefficient B would be

obtained by first plotting the temperature of the Peltier against the voltage of the tip, then the

line of best fit of the graph represents the conversion coefficient B.

25

30

35

40

45

50

55

60

4

4.5

5

5.5

6

6.5

7

7.5

8

8.5

9

220 270 320

Pe

ltie

r Te

mp

era

ture

(℃

)

Pro

be

Vo

ltag

e (

V)

Time (s)

Probe

Peltier

28

The conversion could only provide the change in temperature in ℃, it does not give the

information for the absolute temperature of the thermal map. The reason is the detection circuit

is a balanced bridge circuit, making knowing the actual voltage difficult.

29

Chapter 3 Experimental method

This chapter is separated into two parts. Part I starts with describing the SThM instrument and

how the AFM is modified into an SThM. Then the selection of the samples will be discussed.

Part II describes the procedures of the experiment, it will start with the preparation of the

sample, the tip and the SThM; then move onto the procedure of force measurements and

thermal measurements.

Part I: Instrumentation and the preparation

3.1 SThM instrumentation and integration to AFM.

In chapter 1 the principles of AFM and SThM were described, the fabricated resistor probes

require a power supply and a voltage detector for monitoring the temperature changes. The

AFM probe holder needs to be modified to provide electrical contacts for the current to pass

through. The sample holder needs to be modified to provide the ability to heat up the sample

for the calibration of the probe or SThM operating in passive mode. The SThM instrument at

the University of York is used in this thesis, the modifications to the AFM are shown in Figure

3.1.

30

Figure 3.1 A photograph of SThM set up at the University of York. Including the data logger, probe

power supply, Peltier power supply and detection circuit, the vacuum facility and the AFM. The AFM

control PC is the main control for the AFM.

The AFM used in this project is a JEOL 5200 atomic force microscope, the vacuum facility is

from the original AFM which has not been modified. The vacuum dome is used for providing

high vacuum environment by connecting to a pump. The probe power supply is designed to

have a small current to protect the probe. The AFM sample holder is modified to have a Peltier

heater, a device making use of the Peltier effect to generate heating or cooling at the electrical

junction. The power supply for the Peltier controls the temperature heating of the sample holder.

The Peltier power supply is connected to a 4-pin connector to the sample specimen inside the

AFM. The reading on the Peltier power supply is used for thermal calibration to convert voltage

into temperature. The feedback AFM module is used to switch between the thermal and force

feedback, the data logger computer is used to monitor the probe current. The detail of

calibration process will be discussed later in this chapter.

31

The thermal probe holder was specially designed and produced by Mr John Emery in the

Electronics Workshop at the University of York. The comparison between the thermal probe

holder and the contact probe holder is shown in Figure 3.2.

a) b)

Figure 3.2 a) A comparison between the thermal probe holder (left) and the contact probe holder (right).

b) A photograph of the thermal probe connector with a thermal probe attached.

From figure 3.2a, the design of the thermal probe holder is based on the shape of the contact

probe holder, this is to ensure it fits in the JEOL AFM. On the holder, there is a printed circuit

board with a 4-pin connector to power the probe and a Peltier heater, this is shown in figure

3.2b as well as the two thin gold pins that connect the probe with the power supply. The design

was improved later by having glue placed at the gold pins to increase the strength, the glue

position is labelled in figure 3.2b). Since the data for this project has collected with the new

design, the effect of the probe holder design to the measurements could not be measured.

The power supply for the probe is connected via the thermal probe holder, the probe voltage

signal is connected to the data logger and to the feedback module for recording the change in

probe temperature. The power supply/detection circuit is a balanced bridge circuit, designed

by Prof. Weaver from the University of Glasgow [32]. The circuit is designed to prevent the

probe breaking as well as increasing the signal to noise ratio.

There are several causes that might break the probe, for example static electricity from the skin

or any small shock from inside the circuit. The reason for this is the thermal junction of the

32

probe is small, when there is a high voltage applied across the resistor, the heat generated due

to Joule heating would melt the resistor and break the circuit. Before the experiment, the

detection circuit of the probe has to be balanced by the power supply fine adjustment, so that

the change in voltage due to temperature are more easily measured. The circuit diagram is

shown in figure 3.3.

Figure 3.3 A circuit diagram of the power supply of the probe. The probe is represented as a variable

resistor as each probe will have a variation in resistance. The arrow showed the two variable resistors

that controls the main voltage applying to the tip and the fine adjustment to the voltage, labelled in the

diagram. [34]

The power supplies for both Peltier specimen heater and the probe were connected to a data

logger that is connected to a separate laptop. The reason is a separate computer system could

reduce the noise picked up from the AFM system. The detection signal for the probe would

also feed into the AFM feedback circuit. This is because the AFM has the ability to record the

change in temperature while measuring the topography. The connection for this setup is

showed in Figure 3.4.

33

Figure 3.4 The AFM feedback module panel showing the cable connection and the switch for feeding

the thermal signal into the AFM.

The probe voltage signal was connected to the force channel. It controls whether the AFM was

making measurements in normal AFM mode or in thermal mode. The force and thermal signal

is controlled by the switch indicated in figure 3.4. The switch enables the thermal signal to be

fed into the AFM for measuring the topography along with the thermal signal.

34

3.2 Sample selection.

The choice of samples was decided to cover a wide range of thermal conductivity and

mechanical properties. In the force measurement, it is particularly important to have different

material hardness. It is also interesting to study the effects of roughness and hydrophobicity.

The materials were sourced internally through different research groups at the University of

York Physics department, the properties varied from different methods of manufacturing and

different structure of the material. The table 3.1 displays the typical values of the samples, the

actual values vary from the manufacturing of the materials. If any calculations are required,

measurements should be made for the specific sample.

Material

Thermal

Conductivity (W/m⋅K) Hardness (Mohs)

Elasticity

Modulus (GPa)

Doped 6H Silicon Carbide (0001) 420.00 9 302

Gold (bulk) 314.00 2.5 79

Silicon 124.00 7 179

Mica 0.53 2.5 170

PTFE 0.20 N/A 0.4

Table 3.1 A table summarising the properties of the materials chosen for this thesis. The table includes

the thermal conductivity, hardness and the elastic modulus of the samples. [35], [36], [37], [38]

Teflon (PTFE) has the softest surface and the lowest thermal conductivity. The softness makes

it challenging for making measurements for both topography and temperature. As the surface

is soft, the deformation of the surface is expected from the tip. Mica is a good material for AFM

and SThM due to its layered structure and smooth surface. It has low thermal conductivity and

a relatively hard surface, this covers the lower range of thermal conductivity.

Silicon is a substrate with a 300nm silicon oxide layer, the thin film gold sample used in this

project is fabricated on the silicon sample. [39] Silicon is a semiconductor with a hard surface

and high thermal conductivity. The hardness of the surface makes it more difficult to deform,

35

therefore the temperature changes would be less dependent on the increase of contact area in

contact.

Silicon carbide is the hardest material from the set. It has the highest thermal conductivity to

cover the 400 W/m⋅K range. It is used in calibrating the sensitivity of the cantilever. The hardest

surface would cause least deformation for thermal measurements. However, it could potentially

damage the probe as the Pd coating is soft.

Thin film gold is the sample for testing the technique, it is a thin film conductor fabricated on

silicon. The thin film of gold is 150nm thick grown on a silicon substrate and patterned by e-

beam lithography. Between the gold and silicon, there is 8nm thick layer of chromium at the

interface to improve the adhesion of gold on the silicon. The sample was grown by Dr Vick at

the University of York and patterned at the University of Leeds. [39] The measurements for

this project will be using the electrical contact pads around the outside, which is an area that

does not have dedicated fabrication pattern.

The challenge is to find the thermal conductivity of this sample, as it is not a bulk material, the

conventional gold thermal conductivity will not be valid. The thin film gold is expected to have

a harder surface than PTFE, this is because metal should be harder than polymers. However,

because the gold is a thin film sample, the surface hardness and thermal conductivity are also

expected to be different from the bulk materials.

36

Part II: Experimental procedures

3.3 Preparation for the force and thermal measurements

The Scanning Electron Microscope (SEM) is used in this project to serve two purposes, the

first is to measure the dimension of the probe for calculating the spring constant, second is to

verify the tip status. Figures 3.4 shows the result from a typical SEM experiment of a thermal

probe.

a) b)

Figure 3.5 An SEM image illustrating a) the width and the length measurements from top view, b)

thickness measurements from the side view.

The dimensions of the probe required for the spring constant calculation is described in

equation (9), where the width, length and thickness measurements are required, as shown in

Figure 3.5a and b). Different specimen holders were required to measure each of the

dimensions where a flat specimen holder was used for measuring the width and length of the

probe and an angled specimen holder was used for measuring the thickness.

The dimensions were obtained by measuring directly using the SEM software. The SEM

provides a low instrumental error when measuring the dimensions. However, the shape of the

probe is not ideally uniform, for example, the thickness of the cantilever at the tip end is usually

thinner than the mounting end and the shape of the cantilever is not perfectly rectangular. When

37

estimating the spring constant with the dimensional method, the thickness and the length

contribute most in equation (10) because of the power factor.

The cantilever spring constant was calculated using the values estimated from the SEM for

each probe. The thermal probe cantilevers were assumed to be made of pure silicon nitride and

the contact probe made of silicon. The Young’s modulus of silicon nitride and silicon were

looked up [36] and the values for calculation was taken at the midpoint of the range given. The

error of Young’s modulus is determined by this range. The cantilever is combined with other

substances for instance the gold connection pad and the Pd resistor, however the effect on the

Young modulus is negligible. The total error was worked out for each variable in equation (9)

with multiplication and addition of the quantity, the error will be presented as a percentage

error.

a) b)

Figure 3.6 The estimation of the tip apex of a) the thermal probe and b) the contact probe.

The tip apex radius is estimated while measuring the thickness of the tip, this is illustrated in

figure 3.6. The purpose for this is to compare the tip size between the contact and thermal probe,

in order to compare the quality for the topography and roughness for the samples. The thermal

38

probes were too fragile to be cleaned and should be kept and operated carefully under a clean

environment. The SEM was also used to verify the condition of the tips before a measurement.

The samples were small enough to fit on the AFM Peltier holder, typically the size is about

3mm on the side for a squared shape sample. The samples were first cleaned by placing in

isopropanol inside an ultrasonic bath for 10 minutes, then dried with an air blower. This

procedure was performed every time before any measurements were taken, this is to ensure

there were no obstacles on the sample surface. The mica sample did not require any ultrasonic

bath, this is because mica had a layered structure and can be cleaned, the cleaving process for

mica was simply to peel off the top layer with tape.

The samples had different thickness and the layout for the samples on the sample holder

required careful planning. When the AFM was measuring the thinner samples, the thicker

samples needed not to obstruct the cantilever. This configuration of the samples is shown in

Figure 3.7.

Figure 3.7 The figure of the sample arrangement on the heater.

The tip measuring direction labelled in Figure 3.7 indicates the direction of the tip after the

sample specimen was inserted inside the SThM. The PTFE and gold on silicon samples were

39

thicker than silicon carbide and mica, in principle the thicker samples should be further away

for scanning to prevent obstruction when scanning. In the earlier stage of the experiment, the

samples were placed on the original AFM specimen holder with no Peltier heater integrated. It

was then discovered that the AFM could not scan the thinner samples surfaces. The reason for

that is the probe holder was modified for the thermal probe, which offsets the z direction limit.

The silicon carbide and mica were then lifted up by placing a silicon bar underneath. With the

silicon bar in place, both samples were thicker than PTFE and gold on silicon, hence the

arrangement in figure 3.7. At the later stage of the experiment, the AFM specimen holder was

modified to have a Peltier heater integrated for the ability to do thermal calibration in vacuum,

but the layout of the samples was kept. The samples were shifted to one side of the specimen

holder, the purpose for this was to leave an area for performing thermal calibration with the

probe. The calibration procedure will be discussed later in this chapter. The sample specimen

would then be inserted into the AFM and connected to the power supply.

40

3.4 Methods of topography measurements

The electrical resistance of the thermal tip should be measured before and after inserting into

the probe holder. Although the SEM image of the tip should verify whether the tip is damaged

or having any impurities, the electronic connection is verified by the resistance measurements.

The power supply box was connected to the probe holder while inserting it into the AFM. The

power supply for the probe is a balanced circuit; the procedure for balancing the circuit is to

apply a small current less than 0.1mA, when the voltage of the probe is increased as shown on

the data logger, the voltage is then set back to near 0V by adjusting the offset dial on the power

box. After the power box is balanced, then the current was slowly increased to 0.6mA and

0.8mA. The current was chosen to improve the signal to noise ratio while preventing damage

to the tip. The reason for slowly increasing the current is to avoid the sudden electrical shock

that can damage the resistor at the tip. The data logger monitored the voltage in case of

overheating and circuit damaging. The instrumental error is 0.05mA since the current reading

relies on the precision of the engraving on the knob, the only error estimation is half of the

smallest division on the knob. The error is more significant when comparing the thermal results.

The laser adjustment was done once there was a current passing through the probe. This is

because when a current passed through the probe, the Joule heating would bend the cantilever

and the laser spot will need re-adjustment, hence the probe current balancing was done before

the laser adjustment. The laser spot was set to reflect from near the edge of the probe, the laser

signal represents the cantilever deflection caused by the sample surface structure, therefore

having the laser spot closer to the tip provides a more accurate topographic image. The

photodiode also required adjustment for the largest signal of the probe, for thermal probe, the

typical signal is about 3V and the signal for contact probe is larger. The reason is that the

contact probes have a larger reflective surface than the thermal probes and hence the more laser

beam is reflected.

41

The laser signal could be different every time performing the experiment even if the same probe

is used each time. This is because when the probe is inserted to the holder, the positioning of

the probe will be different each time and the laser will not be reflected at the same area of the

tip and hence the variation in the laser signal. The laser signal is adjusted to collect as a high

voltage as possible to improve the signal to noise ratio. If it is at lower voltage signal, the

signal-noise ratio for the cantilever deflection will be lower and reduce the precision of the

force measurements. Note that there is a significant amount of laser signal heating observed

during the setup of the tip. This could contribute to the temperature difference during the

experiment, which should be taken into account as a possible source of error if the laser position

moves during the experiment.

For experiments performed in vacuum, the vacuum dome should be placed after the laser

adjustment and be pumped down overnight. The vacuum is pumped overnight so that the pump

and the pressure is stable before performing any measurements. During the pump down, the

laser and the probe power were advised to be off after the laser adjustment. The laser could

not be adjusted after the vacuum dome is placed, therefore it should be done in advance. The

vacuum should reach 10−4 to 10−5mbar after one night. The specimen was then manually

approached so that it was close to the probe. The process is observed by an optical microscope

and it is important that the sample does not hit the probe. The approach process is then

continued using the JEOL WinSPM software to control the z-piezo tube for the remaining

distance. During the experiment, the laser spot could move on the photodiode. A magnet is

attached on the control knob of the photodiode, the knob could be turned by using this magnet,

while the whole instrument is inside the vacuum dome.

The vacuum is created by placing the vacuum dome on top of the SThM for pumping down.

When preparing the vacuum dome, vacuum grease is used for sealing the gap between the

dome and the SThM, the quality of vacuum grease could directly affect whether the vacuum is

42

sealed entirely. The vacuum pressure was left overnight for stabilisation, however the vacuum

pressure should be monitored during the experiment. The reason is the vacuum reduced the

heat path for cooling the tip. A change in pressure was observed from 10−5mbar to 10−4mbar

and this change did not cause a significant effect on the thermal result.

The quality of the topography was determined by the scan size and the clock rate, while the

filter setting was set at 50kHz by default for both force and thermal measurements. The scan

size is the dimension of one side of a square and the clock rate is the speed for the probe moving

across the area. [29]

The topography scan was chosen to a scan size of 500nm for roughness analysis. The scan size

of the topography should be enough to present the overall sample surface while retaining spatial

resolution for making thermal measurements. The clock time should be optimised for a balance

between scanning time and quality. A slow clock rate can result in a scanning duration of 30

minutes per topography scan. In this project, the scanning duration is optimised to

approximately 10 minutes per scan. The probe requires a minimum time window to respond to

the surface. Such minimum requirement can be found by scanning the sample surface at

different rate and thus determine at which the quality of the scan does not improve significantly

further by inspection.

The thermal probe was expected to have a larger contact area than the contact probe, the

scanning size and the clock rate were optimized for both probes to have the same setting for

comparison. The scanning size and the clock rate in this project was optimised to 500μm with

500μs scanning time for both contact probe and thermal probe. Thermal measurements were

measured by enabling the probe power signal input to the AFM feedback hub.

After setting up WinSPM, the scan was commenced to collect the topography. In addition, after

each scan, the laser signal must be checked. Particularly after scanning on a hard sample with

43

a soft tip, it is possible to cause deformation to the tip after a scan therefore a check on laser

signal would ensure the result is representative. The topography image often required

processing before analysing. This is to improve the contrast of the image to enhance the details

on the topography. The appropriate height scale should be chosen to extract enough detail for

roughness analysis.

44

3.5 Force measurement and roughness procedure.

The force measurements were used to measure the adhesive force of the sample. The roughness

of the sample surface would affect the measurements, therefore when performing the force

measurements, a clean smooth area of the topography should be chosen. The displacement for

the specimen is the distance range for how far away the stage should move and the clock rate

determines the approaching velocity of the sample. These variables needed to be set in the

WinSPM software before measuring the surface force. The displacement value was done by

trials and errors because it was different for each sample. The optimum displacement should

show a continuous curve with the following elements: the starting position, the snap in point

and the snap out point, which were indicated in figure 2.2. The author started by moving the

tip away from the sample for 1000 nm, then decreasing the distance by 100nm to get the

optimum displacement. The clock rate was set to 1ms.

In section 3.3, the spring constant of the cantilever was calculated from the SEM measurements.

The force conversion that was described in equation (6) requires the measurements of

sensitivity, α , as defined in equation (7). The sensitivity measures the displacement per

deflection signal. If the sample surface deforms when the tip is in contact, it would misrepresent

the deflection signal of the cantilever. The sensitivity is chosen to measure from the force

curve of silicon carbide and then apply the same sensitivity to all other samples. Silicon carbide

has the highest surface hardness from the sample set that gives the least surface deformation.

45

The sensitivity was taken as the line of best fit of the retract section on the force curve in the

linear range of data as shown in figure 3.8. The reason is due to the nonlinear piezoelectric as

shown in figure 2.2. The measurements were repeated at all points take for each area and the

standard deviation used as an error.

Figure 3.8 A schematic diagram showing the measurements made in a force curve. The difference of

𝑉𝑚𝑖𝑛 and 𝑉0 is the adhesive force dF being measured. The line of best fit for sensitivity measurements

is noted.

The V0 from equation (6) was measured individually for each sample and each curve. The V0

was measured by averaging the V at the retract region after the zero point, this is shown in

figure 3.8. The region is chosen to avoid the vibration caused by the snap out of the cantilever.

Each force curve was converted individually as the V0 could be different each time. The

adhesive force measurements were made by measuring the force of the cantilever when the tip

snapped out during retraction. The force measurement, dF, was taken as the difference between

the minimum point, Vmin, and the reference potential, V0, after the force curve is converted into

Newton units. The principle is the same as shown in figure 3.8.

46

The force curves were repeated at 3 different areas for each sample. Each area was repeated 3

times and averaged for presentation. All 3 areas were compared and found to be the same

therefore the author was able to average the total 9 points of measurements for reducing the

random error. When the areas are different, the areas were not averaged and this will be noted.

The force measurements are localised measurements, when repeating the experiment, different

parts of the sample surface were chosen to give a fuller representation. For each sample, the

dF at each area was averaged and the error is worked out through the standard deviation. Then

the dF of the sample was obtained by averaging the dF from the three areas. The total error for

the force would be weighted from the errors measured in each area. When comparing the

adhesive force, the error caused by the spring constant was not counted, this is because the

measurements for each sample were performed with the same tip. The spring constant error

should be accounted for when comparing the results using different tips, and the adhesive force

should be normalized accordingly. There are other factors that would affect the adhesive force

measurements. The topography was analyzed before picking the areas for force measurements

to make sure the areas were representative of the surface structure.

47

3.6 Calibration of thermal probe and measurements procedure

As noted in Chapter 3.3, the purpose for thermal calibration is to measure the thermal

sensitivity of the probe, converting voltage to ℃ for analysis. This is because the probes are

not identical and their electrical resistance varies. This resistance variation causes the

difference in thermal sensitivity, therefore the calibration process is required for each new

probe used. The probe resistance was measured by the multimeter before it was inserted into

the probe holder.

The calibration coefficient is measured before starting the force and thermal experiments.

When there is a change of probe, it will require another calibration because each probe will

have different thermal sensitivity. In addition, the tip is observed to have a change of the sensor

shape, therefore when the tip has been used for many experiments, the calibration should be

remeasured. A Peltier heater was used for the thermal calibration with a Pt100 thermometer for

monitoring the heater plate temperature. The Pt100 thermometer, shown in figure 3.7, is a

resistance thermometer which uses the linearity of resistance with temperature for thermometry.

The error of the probe temperature and the voltage are the instrumental errors from the data

logger. Since both variables are collected in the same device, the instrumental errors are the

same.

In figure 3.7 the reserved space on the specimen was prepared for this calibration process. First

a current in the range of 0.6mA to 0.8mA was passed through the probe. The probe would then

approach to the sample, the scan size was set at 0nm with a slow clock time, this would activate

the force feedback on the AFM. The probe would remain in contact with the sample surface

during the calibration so that the vibration effects due to thermal transport were reduced. The

clock time was dependent on how long the calibration was taken, in air the clock time was set

48

to 500μs and for vacuum it was set to 1ms. A longer time is required in vacuum as the signal

to noise ratio is lower.

The Peltier heater was set to be 60 ℃ for heating. When the Peltier reached about 60 ℃, it was

switched off for the cooling process. This procedure is to verify there is a consistent calibration

for both heating and cooling. The temperature range was chosen to give a wide range for the

probe to cool down. The thermal calibrations for both environments were repeated 3 times for

each probe or change of environment. The data logger collected the probe voltage and the

Peltier temperature against time in seconds. Figure 3.9 shows a typical thermal calibration

result from the data logger.

Figure 3.9 A typical result from the data logger for thermal calibration.

In vacuum, three different methods were used to optimise the setting. The first method was to

heat up the Peltier to 60 ℃ and allow it to cool down by the environment. A temperature jump

was observed during cooling with this method, indicated in figure 3.10. The cause of the

temperature jump could be an instrumental error, however it was not identified. The second

attempt was to heat up the probe by manually turning up the Peltier temperature to 60℃, and

25

30

35

40

45

50

55

60

4

4.5

5

5.5

6

6.5

7

7.5

8

8.5

9

200 300 400 500 600

Pe

ltie

r Te

mp

era

ture

(℃

)

Pro

be

Vo

ltag

e (

V)

Time (s)

Probe

Peltier

49

then control the cooling down process by manually reducing the power of the Peltier. The third

attempt was an optimised version of the first attempt by heating the probe to 40 ℃ to avoid the

instability. Although this same method was attempted in vacuum, the thermal calibration

coefficient gave a false impression of the temperature conversion which will be discussed in

chapter 5.

Figure 3.10 Figure of thermal calibration in vacuum heated at 60℃, the temperature jump during

cooling is marked.

The cooling range was chosen by inspection for plotting the probe voltage against the Peltier

temperature. Three graphs of the probe voltage against the Peltier temperature were plotted for

each repeated measurement and a gradient was obtained by the line of best fit. The gradient is

the probe voltage to temperature conversion for the experiment. The error for the gradient will

be calculated from the standard deviation of the repeated values. Figure 3.11 demonstrates the

method for obtaining the conversion coefficient.

50

Figure 3.11 A typical measurement of probe voltage against Peltier temperature, a line is fitted for

estimating the conversion coefficient from voltage to temperature.

A thermal hysteresis loop was observed during the analysis of the calibration, which will be

discussed in chapter 5. The 0.6mA current was chosen to avoid overheating the tip. However,

periodic noise was observed during the thermal measurements in vacuum so a 0.8mA current

was used later to improve the signal to noise ratio. The source of the noise was not found during

the thesis. This calibration method is only valid for calculating the change in temperature,

because of the balanced bridge circuit the absolute temperature is not measured.

The thermal calibration was undertaken before thermal measurements in both air and vacuum

and, as it was shown in figure 3.7, the samples are on the same specimen as the Peltier. During

the calibration process, the sample was heated, which causes a problem for the thermal

measurements. If the sample temperature is higher than the tip, the thermal experiment will not

be valid therefore, the sample must be cooled down to a stable temperature before making any

thermal measurements. The sample cooling was monitored by the Peltier signal through the

data logger. The samples will take longer to cool down to a stable temperature in vacuum, this

is because cooling is only via radiation.

y = 0.12x + 1.8R² = 0.9993

4.5

5

5.5

6

6.5

7

7.5

8

8.5

9

25 30 35 40 45 50 55 60

Pro

be

vo

ltag

e (

V)

Peltier Temperature (℃)

51

The thermal measurements procedure is similar to the force measurement described in the

chapter 3.5. Once the topography of the samples has been measured and the area is chosen, the

thermal measurements were made by feeding the thermal information into the AFM feedback

module. The data logger was used to monitor the probe voltage during the thermal

measurements. This is to record the change in temperature when the tip is far away from the

sample and to monitor the probe in case of short circuit. The clock setting and the tip

displacement for thermal measurement should be the same as force measurements, this is to

ensure both the force and thermal measurements are comparable.

52

Figure 3.12 Illustration showing a close up of a thermal hysteresis with explanation of how to measure

the change in temperature.

A generic shape of the thermal curve result in air is showed in figure 3.12. The thermal curve

forms a hysteresis loop, showing the displacement on the x axis and the temperature on the y

axis. Figure 3.12 shows a measurement taken in air where the temperature drops suddenly as

it gets in contact with the sample. Figure 3.12 also shows how the change in temperature is

measured.

When the tip retracts, the adhesive force on the sample surface will keep the tip in contact.

Since the tip is constantly retracting this causes a bending of the cantilever, until the retract

force is sufficient to overcome the adhesive force at which prompt the tip will then snap out.

After the tip has snapped out, the distance between the tip and sample will depend on where

the stage has got to in the retract cycle. On the data logger, the snap-out change in temperature

will be larger than the snap-in change in temperature. The snap-in change in temperature is

more representative of the thermal conductivity. This is because the snap-out change in

53

temperature is affected by the adhesive force varies between samples. The snap-in change in

temperature is less affected by the mechanical properties of the samples, hence it is more

representative of the thermal properties. Since the snap-in change in temperature happened

during the approach process, we will call this the ‘approach temperature’ and it is marked as

‘dT approach’ in figure 3.12.

The approach temperature measurement is marked in figure 3.12. It is made by measuring the

average temperature of 10 points before and after the tip made contact with the sample surface,

then the difference of these values is the approach temperature. Ten points were chosen as a

balance between averaging over as many points as possible to reduce noise, but making sure

that the value is not affected by real temperature gradient due to the cooling of the tip.

The range of points for measuring the change in temperature is showed in figure 3.12. When

analysing the data, the force curve will be plotted on the same axis with the thermal curve. The

intersection of both curves shows the snap in and snap out point of the tip. The range of points

is then chosen at this intersection by inspection and the range of points will be used for

calculations. The error is estimated by the standard deviation of the measured dT through the

repeated values. There are some parameters to be aware of for the temperature measurements,

for example, the laser signal and the electrical current through the tip will contribute to the

temperature reading. A significant amount of laser signal heating the tip was observed during

the setup of the thermal calibration. This effect is neglected when analysing the change in

temperature in this project, however it should be taken into account when working out the

absolute temperature in the system.

54

Chapter 4 Topography and force curves measured using contact mode

and thermal probes

This chapter presents the results for the mechanical measurements made by the SThM. The

aim of these mechanical measurements is to investigate the relationship between the adhesive

force and the hardness and elastic modulus. Understanding the topography of the sample and

the material properties should provide an aid to interpreting the thermal measurements. For

example, the surface hardness can affect the contact area of the tip and cause a change in

thermal conduction. The force measurements are also used to verify the contact point of the tip

in the thermal measurements, hence the study of the mechanical properties is important for

analysing the thermal measurements too.

This chapter presents the force measurements results including the probe dimensions, the

calculations of the probe spring constant and the force measurements of different sample using

thermal probe. This chapter will conclude by comparing the roughness analysis with the

samples and comparing the force measurements.

55

4.1 Physical dimensions from SEM and spring constant results

The dimensions of the probes were measured using the SEM, there were four different probes

used in this study: three thermal probes and one contact mode AFM probe, an SEM picture for

all the probes are labelled and shown in Figures 4.1. The measurements from the contact probe

were used as a reference for comparison.

a) b)

c) d)

Figure 4.1 shows the SEM image for all probes used in this project. Figure a)-c) are the thermal probes

A-C and d) is the contact probe D, the figures above were measured with the scale bar of 10 μm.

The figure 4.1 shows the SEM image of the four tips that were used in the experiment. The

SEM images were measured with the scale bar of 10µm. The thermal probes A – C all have a

similar shape and dimension since they are same type of probes. The contact probe D is

showing to be narrower compared to the thermal probes. This is because there are no electronic

contacts required on the contact probe.

56

Table 4.1 presents the SEM measurements for each probe. The table is presented in two parts,

the top table gives the results of the dimensions of the probes measured by SEM. The bottom

part is the calculated spring constant from the dimensional method discussed in chapter 3 along

with the current applied during the thermal experiments.

Unit Symbol Probe A Probe B Probe C Probe D

Young's Modulus 𝐺𝑃𝑎 𝐸 290±30 290±30 290±30 150±20

Width μ𝑚 𝑤 116±1 118±2 113±1 38±1

thickness μ𝑚 𝑡 1.0±0.1 0.9±0.1 0.56±0.01 3.4±0.1

Length μ𝑚 𝐿 148±1 151±1 144±1 134±1

spring constant 𝑁/𝑚 κ 2.6±0.3 1.6±0.4 0.5±0.1 23.1±0.2

Current used 𝑚𝐴 𝐼 0.6±0.05 0.6±0.05 0.8±0.05 N/A

Resistance 𝑂ℎ𝑚 𝑅 336±0.5 331±0.5 340±0.5 N/A

Tip apex radius 𝑛𝑚

N/A N/A 59±20 47±20

Table 4.1 Dimension measurements and spring constant calculation for all the probes. [35], [36], [38]

Table 4.1 shows the measured dimensions and the calculated spring constant for each probe.

The contact probe D is the contact probe that is used for reference, its dimensions, Young’s

modulus and the spring constant are expected to be different from the thermal probes. There

are several direct comparisons that can be noted in table 4.1. The Young’s modulus values were

looked up from the material data reference [36], [38]: the thermal probes were approximated

to 290 GPa and the contact probe to 150 GPa. The dimensions of the contact probe D are

smaller than thermal probes, except the thickness which is approximately 3 times thicker than

the thermal probe A.

When comparing the spring constant between probes A – C, the results show a variation from

probe C with 0.5 N/m to probe A with 2.6N/m. It is noted that there is an increasing trend of

thickness with the spring constant, this can be shown in the calculation of spring constant in

57

equation (10). The spring constant is directly proportional to the Young’s modulus, width of

the cantilever and the thickness; the power factor in equation (10) makes the thickness more

important to the spring constant calculation.

The spring constant assumed all the probes are rectangular shape therefore the calculated value

is only an approximation as a guide for comparison. The Young’s modulus for thermal probes

is approximated as silicon nitride, note that the fabricated gold connections could affect the

effective Young’s modulus of the cantilever. Since the spring constant was used as an

approximation, the effects of the gold were neglected. The Young’s modulus for the spring

constant was looked up from the material tables and was provided as a range of values. [35]

The median value of the Young’s modulus was used in estimating the spring constant and the

range was used as an error, this gives approximately a 10% error for the thermal probes and a

13% error for the contact probe on the Young’s modulus.

There was a challenge when measuring the thickness of the thermal probes thickness, probes

A and B were found to have an impurity on the cantilever as this is shown in figure 4.2.

Figure 4.2 The impurities on the cantilever of probe A, the impurity is located towards the holder on

the left-hand side of the picture. This could potentially affect the spring constant estimation.

58

The thickness of the cantilever quoted in table 4.1 neglected the impurity shown in figure 4.2.

This is based on the presumption that the mass of the impurities relatively low such that it

does not cause a significant impact on the calculation. The error on thickness accuracy was

the same in all thermal probes, this is because the magnification was set to be the same.

During the SEM measurements, a thermal drift was discovered when the scale bar reaches

less than 100nm, this drift only affects measurements in fine scanning mode. A fast scanning

mode was used in measuring the tip apex, this gives a lower resolution image but the results

are more representative of the probe shape and dimensions.

The tip apex radius is an attempt to estimate the tip contact area, this will only be used in

comparison between contact and thermal probes and was not required in any calculations.

The tip apex was only measured for the contact probe D and the thermal probe C, this is

because thermal probes A and B were damaged during the experiments. The apex radius of

the thermal probe C is 58.9nm and for contact probe D is 47nm. The contact probe apex was

expected to be significantly smaller than the thermal probe, however the apex sizes are

similar in the measurements. From this comparison, the results suggest that the topography

spatial resolution between both probes C and D will be similar since it is dependent on the tip

apex size. The image of the tip also shows that there is a soft edge of the end of the tip, this is

because of the diffraction on the SEM. The error was estimated between the diffraction area

shown on the image and compared to the scale bar of the image.

The thermal probes resistance was measured before the experiment to ensure the probe was

not damaged. The electrical resistance was also measured after the probe was inserted to the

probe holder, this is to ensure the connection between the probe and the holder is secure.

There was some instrumental failure during the experiment, the electrical signal for probe A

was lost during the experiment in vacuum and the probe was replaced with probe B. The

59

resistor on probe B was found peeling off from the tip in SEM scan after a set of force and

thermal experiment. This is shown in Figure 4.3. The probe C was used in repeating the

experiment. The contact probe D was used as a reference for comparing the effects with

thermal probe.

Figure 4.3 The SEM image of probe B with layer of palladium resistor coating peeling off after

measuring a set of thermal measurement. The scale bar of the figure is 100nm.

In summary for this section, the spring constant of all four probes are presented and the error

was discussed. The measurements also showed that the thickness of the cantilever dominates

the spring constant calculation. The tip apex was only measured for two probes, the difficulties

and the error were also discussed.

60

4.2 Topography and roughness analysis

The topography is required to complement the force and thermal measurements, a topography

scan with high resolution can improve the overall inspection of the sample surface. In section

4.1, the results showed that the contact probe and the thermal probe have different spring

constants and different tip dimensions. The first result is to compare the topography measured

by the different tips. Figure 4.4 shows the different topography measurements between contact

probe and the thermal probe.

a) b)

Figure 4.4 Silicon carbide topography measured with a) contact probe and b) measured with thermal

probe C. The figures represent a similar area of the silicon carbide.

Both the contact and thermal probes were operated in air when producing the topography in

figure 4.4. The marks on figure 4.4b) are the locations where the adhesive force and the thermal

measurements were taken. The contact probe should give a more detailed image of topography

if it has a smaller tip apex size. However, in section 4.1 the tip apex radius was showed to be

similar between the contact probe and the thermal probe, hence the topography in figures 4.4

does not have a significant difference. In addition, the thermal tip is more capable in detecting

smaller features with the thermal image, hence the roughness analysis will also be using the

thermal probe.

The topography procedure in figure 4.4 should ideally measure the same area on the sample,

however to measure with two different probes, a change of the probe holder is required and

100nm

1.99 nm

0.00 nm

5.80 nm

0.00 nm

61

this resulted in a change of measured area on the sample. The only attempt to return to the same

area is, during the change of probe holder, the sample specimen is fixed in place to try and

maintain a similar measuring area when a new probe is inserted. However, with the scanning

size of 500nm, it is impossible to mark out the exact area for repeated scanning using the optical

microscope, therefore the result above can only be compared within the sample. The tip apex

radii were estimated after both force and thermal experiments.

In figure 4.4, the observation of the wavy pattern is visible on both diagrams. This suggests

that the interference is not caused by the type of tip is used, since it is also observed in most

topography and thermal map results. It is suspected there is an interference caused by the laser

signal, however no investigation was attempted to resolve this phenomenon as the single point

measurements of force and temperature were not affected.

The average height across the scan area is used to compare the flatness of the surface. The

SThM measures the height of the sample from a reference point and marked as 0nm. The RMS

roughness is the standard deviation of the height at a point from the average height, this gives

a measure of how much variation of height there is across the surface which is also a measure

of roughness. The other parameter measured is an estimate of the typical width of the surface

features taken from the line scans.

The average height of the silicon carbide measured with the contact probe (Figure 4.4a) is

1.02nm with an RMS roughness of 0.35nm. The average height measured with the thermal

probe is 1.66nm with the RMS roughness of 0.37nm. By converting the RMS value to

percentage of average height, the contact probe gives a surface variation of 34% while the

thermal probe gives 22%. This study was an attempt to investigate the difference in contact

probe and thermal probe, however since the scanning areas are different, the result would

require repeated measurements for further deduction. As the contact probes are not providing

62

much additional information, the thermal probes are used for the topography analysis of the

samples so that they match the thermal scans.

The topography result for each sample will be presented in the following section. The results

will be presented with the topography and with a profile for roughness analysis. The

topography was measured using the thermal probe, for the convenience of obtaining the force

and thermal measurements later. The presentation will include a list of numerical results, this

includes the average height of the topography scan area, the RMS roughness of the average

height and an estimation of the dimensions of the surface features. The line scan positions were

chosen to be representative of the area and two of these were measured to estimate the feature

size for each sample. The force curves are presented at the bottom of the figures, it is the

average of all 9 curves taken from three different areas. The left force curve is measured in air

and the force curve on the right is in vacuum. The analysis of the force curve will be discussed

in the next section.

63

Average height: 3.9nm

RMS roughness: 1.1nm

Feature height: 4.8±0.5 nm

Feature width: 85±10 nm

Figure 4.5. Roughness analysis of gold thin film.

Average height: 0.92nm

RMS roughness:

0.22nm

Feature height: N/A

Feature width N/A

Figure 4.6. Roughness analysis of mica.

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rce

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64

Average height: 10.4nm

RMS roughness: 3.4nm

Feature height: 20±5 nm

Feature width: 240±30 nm

Figure 4.7. Roughness analysis of PTFE.

Average height: 1.18nm

RMS roughness: 0.27nm

Feature height: 1.1±0.4 nm

Feature width: 110±10 nm

Figure 4.8. Roughness analysis of silicon.

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65

Average height: 1.65nm

RMS roughness: 0.37nm

Feature height: 1.4±0.2 nm

Feature width: 120±10 nm

Figure 4.9. Roughness analysis of silicon carbide.

Figures 4.5 to 4.9 show an overview of the topography of the samples and the values are

summarised below in table 4.2. The first result presented was the gold thin film, it has

distinctive surface island features visible in figure 4.5. The gold feature width is comparable

to the tip apex radius of about 50nm, the tip radius will limit the lateral size which can be

detected.

The PTFE showed some features from the topography that are measurable, the features have

the largest width from the set of samples measured. The PTFE has the highest average height

of 10.4nm, this indicates that the surface variation is large in comparison to other samples.

Mica picked up some interference noise in the topography, the surface feature cannot be shown

on the topography, this could be that the features are smaller than the interference signal. The

average height is the smallest of all the samples, it indicates that the mica surface is the

smoothest of all the samples.

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66

The result of silicon shows some interference at the top part of the topography, the features can

be seen and measured. The line profile of silicon was measured towards the lower end of the

topography, this is to avoid the interference pattern.

Silicon carbide topography was presented, the result is similar to silicon, where the sample

features were shown. The line profile also shows the noise picked up from the interference.

The next part will be presenting a summary of the numerical results measured from the

topography. Table 4.2 presents a summary of the measurements including the hardness and the

elastic modulus recalled from chapter 3.2.

Material

average

height

(nm)

RMS

roughness

(nm)

RMS

roughness %

Feature

width (nm)

Feature

height

(nm)

Elastic

Modulus

(GPa)

Hardness

(Mohs)

SiC 1.7 0.4 22% 120±10 1.4±0.2 302 9

Si 1.2 0.3 23% 110±10 1.1±0.4 179 7

Mica 0.9 0.2 24% NA NA 170 2.5

Au 3.9 1.0 28% 85±10 4.8±0.5 79 (bulk) 2.5(bulk)

PTFE 10.0 3.4 33% 240±30 20±5 0.40 -

Table 4.2 Summary of the topography of each material.

Table 4.2 presents the data in order of descending elastic modulus for the convenience of

comparing the values between the samples. The samples can be categorised into three different

types. The first type is the soft material, PTFE, it has the lowest elastic modulus and hardness.

The hard-bulk materials of silicon, silicon carbide and mica, all with high values of elastic

modulus. Finally, the unknown deposited material thin film gold, the elastic modulus and the

hardness given are the bulk values, the actual property of the gold thin film is not known.

The average surface height of the hard-bulk materials was found to be similar, this is indicating

that the silicon, silicon carbide and the mica are sharing a similar roughness. From the

topography, all of the materials in this category showed the interference however, only mica

67

does not show any surface features. The reason is the mica features are smaller than the

interference signal.

The average height of PTFE is the highest at 10nm, this indicates that the PTFE has the roughest

surface. The features showing on PTFE also have the biggest width of 240nm. The PTFE and

thin film gold did not show any interference from the topography. The thin film gold showed

some distinctive island features with 85nm in width and 4.8nm high. The feature width is

comparable to the tip apex radius of about 50nm, the tip radius can affect the lateral size that

gives a lower resolution in width. After converting the RMS roughness into the percentage of

the average height, the percentage shows a weak directly proportional relationship with the

elastic modulus.

68

4.3 Force measurements comparison between samples

The force measurements of the samples will be presented in this section. The force

measurements were recorded in voltage, a conversion from V to nN is required for comparison

and analysis, the conversion method is described in equation (6) and discussed in chapter 3.5.

The spring constant was obtained in the chapter 4.2 by inverting the gradient of the retract

region from the force displacement curve. The results are shown in table 4.3.

Probe Sensitivity, α

(nm/V)

%error Spring constant, κ

(N/m)

A 16.94±0.03 0.17 2.62±0.32

B 16.62±0.01 0.06 1.62±0.36

C (in air) 67.1±0.13 0.2 0.50±0.09

C (in vacuum) 56.6±0.1 0.13 0.50±0.09

D 27.5±0.1 0.19 23.10±0.16

Table 4.3 Table presenting the sensitivity a from inverting the overall average slope of silicon carbide.

The sensitivity measures the change in distance against the change in voltage defined in

equation (7), but the force curve measures the voltage against the displacement. Therefore, the

gradient measured on the force curve needs to be inverted for the correct sensitivity. The force

conversion for all samples is done using the sensitivity measured on silicon carbide. The reason

is the thermal probe is made of silicon nitride, if the sample surface is soft, the cantilever will

push into the sample without bending the cantilever significantly, this leads to a false

presentation of the sensitivity. Silicon carbide is therefore chosen for measuring the sensitivity

since it is the hardest material from the sample set, there is less likelihood of the silicon carbide

surface to deform, however, it is possible that the hard surface of silicon carbide will damage

the thermal contact of the tip.

69

The force results in Figure 4.10 illustrate the difference between a thermal probe and a contact

probe. The figure shows the measurements of silicon carbide in air, the force is measured in

voltage and has not been converted.

a)

b)

Figure 4.10 Force measurement results of silicon carbide measured in air with a) the contact probe D

and b) the thermal probe C.

Figure 4.10 a) is a result from the contact probe, the first observation is that the adhesive region

is significantly smaller than that from the thermal probe in figure 4.10b). The contact probe has

much higher spring constant than the thermal probe, the higher spring constant of the cantilever

provides an extra force to overcome the surface adhesive force, resulting in the small adhesive

region for contact probe. In contrast, the thermal probe has a smaller spring constant compare

to the contact probe, hence the surface adhesive force is able to hold the tip in contact. When

the cantilever provides enough force to overcome the surface adhesive force, the tip snaps out

of the surface. As the z piezo tube is moving out during this period the tip is contact with the

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70

surface, this makes the tip returns to a position that is further away than the contact point from

the sample surface when the tip is released.

In figure 4.10 b), the gradient from where the tip is in contact and before the tip snaps out does

not show a linear relationship. This bending of the curve affects the sensitivity measurement

required in equation (7). The sensitivity approximation is estimated using the linear part of the

retract area to avoid the bending. The reason for this observation was not investigated.

Sometimes the limit of the force range was reached, as illustrated in Figure 4.11.

Figure 4.11 A diagram illustrating the force measurements that exceeded the AFM limit. Two

gradients were drawn and the intercepts were used to determining the adhesive force.

In these cases, two lines of best fit were drawn along with the trend of the retract curve for

finding Vmin. The first line is fitted through the retract curve before the AFM reaches the limit.

The second line is fitted at the snap out gradient, this gradient is often fitted for two points only,

this is because the snap out process is too fast for the scan rate. However, this method relies

71

heavily on the data selection for plotting the gradient. The results were inconsistent and have a

large error. The author tried to offset the force range of AFM to avoid this limit, the result was

different and the typical results are shown in Figure 4.12.

Figure 4.12. A diagram showing the typical force measurement result of silicon after the offset of

sensor limit.

Figure 4.12 demonstrates the shape of the force curve from the result of silicon measured in

air. There is an observation of cantilever vibration after snapping out, this is labelled in figure

4.12. The V0 is chosen to avoid this vibration for the value used in conversion. During the

experiment, an unusual shape of the force curve was sometimes observed.

The shape of the curve in figure 4.12 was different to figure 4.11, at the retract area, the flat

region showed a sharp change below the limit, then returned to the flat limit before snapping

out of the surface. This unusual shape of force curve is observed consistently in silicon and

PTFE for both environments, it was also observed for to the thin film gold sample in air, but

not for silicon carbide or mica.

A possible cause for this shape is the tip leaving the sample and then arriving at a contamination

layer of material, before finally snapping out of the surface [40] or it could be an instrumental

effect that has not been identified yet. Although the sample set materials were expected not to

72

have a contamination layer, it is possible to have an extra layer of moisture on the sample

surface. It is also expected that there will be a layer of silicon oxide on the silicon surface and

possibly even some residual resist from the patterning process. The Vmin used in the

calculations will use the furthest point of the tip before it jumped to the flat region, this is

marked in figure 4.12. With the V0 described earlier, the retract force was measured.

Table 4.4 presents the retract force results measured using the thermal probe. The result of

thermal probe C only is presented. The table presents force measurements measured in air and

in vacuum. The results are presented in the order of the descending order of elastic modulus.

Results of thermal probe C in air

Results of thermal probe C in vacuum

Material dF(retract)

(nN)

% error Elastic

Modulus

(GPa)

Material dF(retract)

(nN)

% error Elastic

Modulus

(GPa)

SiC 175±2 1.11 302 SiC 133±5 3.9 302

Si 179±2 0.9 179 Si 153±6 3.8 179

Mica 165±0.3 0.2 170 Mica 144±3 2.2 170

Au 144±0.5 0.37 79(bulk) Au 160±4 2.4 79(bulk)

PTFE 77±1 1.38 0.4 PTFE 145±10 6.7 0.4

Table 4.4 Retract force measurements using thermal probes.

The first comparison is the result between the environments. The retract force is generally

larger in air than in vacuum except for gold and PTFE, which were also inconsistent from

previous result using probes A and B. The reason for air to have a larger retract force is in air,

water forms a layer on the sample surface, which has a high surface force and attracts the tip

to the surface. [40] The gold and the PTFE are the least uniform samples, they have a large

variation across the surface, therefore it is challenging for comparing in air and vacuum because

the tip is at different position.

When comparing the results between the samples, a general trend emerged that the silicon,

silicon carbide and mica have similar results. The silicon consistently has a larger adhesive

73

force than silicon carbide. For one set of data, the force curve of silicon carbide exceeded the

limit of AFM, which gave the shape described in figure 4.11. In this case the silicon carbide

adhesive force was larger than silicon, but the extrapolation method is not as reliable. We are

therefore left with the observation that either the silicon carbide has a smaller value than

expected or the silicon has a higher value than expected. As the silicon value is close to that of

mica it looks more likely that it is the silicon carbide that is lower than expected.

The comparison then moved onto comparing the force value of mica. The force results for these

samples are in general similar. The mica force value is observed to be consistently lower than

silicon carbide in air, but vice versa in vacuum. When comparing the mica force values with

silicon, the force value of silicon is consistently larger than mica in all environments. The

values of silicon and mica are comparable in all environments, this is indicating the silicon

carbide is showing a lower value than expected.

The mica usually returns a higher value than gold, from the table the gold shows a higher value

in vacuum than in mica. The thin film of gold has unknown properties including hardness and

thermal conductivity. Although the gold shows a consistent retract force, it was expected to

have different properties from the bulk material and the island features may affect the variation

across the surface.

The PTFE retract force is observed to be larger in vacuum than in air. The PTFE has a

percentage error of 1.38% in air and 6.7% in vacuum for the retract force, it is significantly

larger than other samples in both environments. Since PTFE has the softest surface, the surface

deformation caused by the tip would introduce variation across the surface that leads to

inconsistent results. The force curves of PTFE measured across the 3 different areas on the

same topography showed a significant variation of the retract force. The retract force error for

one area can be up to 6.2% in vacuum. This variation could be the main cause of error and is

74

showing in both air and vacuum. This is illustrated in figure 4.13, a force result of PTFE

measured in vacuum. Since the both vacuum and air experiment were completed separately, it

was not possible to mark out the exact same area for measurement, and the variation is therefore

greater.

Figure 4.13 Force result of PTFE in vacuum, measured in three different areas showing the variation.

The retract force is the force of how adhesive the sample surface is when the tip retracts, the

explanation of the curve is explained in chapter 2. The next discussion will be comparing the

results to the roughness of the samples. There is not a clear correlation between the retract force

and the roughness analysis. However, when comparing the retract force with elastic modulus,

samples with higher elastic modulus were observed to have a larger retract force, except for

the gold thin film. The gold thin film was quoted as 79GPa for the elastic modulus, however

this is quoted from the bulk value, whereas the thin film value is not known.

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75

4.4 Discussion of the results

This section discusses the challenges of making force measurements and summarises the

achievements with the aims at the beginning of this chapter. The aim for the force

measurements was to investigate the relationship between the mechanical properties, the

adhesive force and the hardness. The topography improved the understanding of the surface

features including the roughness.

The SEM results for measuring the dimension were first presented, the result showed the

difference in characteristic for both contact and thermal probes. The contact probe has a higher

spring constant when compared to the thermal probes. The contact probe cantilever is

approximately 3 times larger than the contact probe, however, the contact probe is about 3-5

times thicker than thermal probes. The spring constant for each probe was then presented.

Probe C was used for the main result presented in this thesis, the spring constant for probe C is

0.5±0.1 N/m. The contact probe did not show a clear adhesive region in the force curve due to

its high spring constant of 23.1±0.2 N/m.

The challenges such as measuring the thickness due to the impurities and the focusing of the

SEM was discussed. The theory for obtaining the spring constant was an estimation, this could

directly cause a false presentation for the absolute value of force. Other methods of measuring

the spring constant described in chapter 2 could be further investigated. For example, the

possibility for using the reference cantilever method to obtain the spring constant could be

investigated.

The SEM was used to measure the tip dimension for obtaining the spring constant, during this

measurement, the tips condition was found to be unstable after being used for thermal and force

measurements. For example, the palladium resistor coating was found to be peeled off after the

thermal experiment, as shown in figure 4.3. This raised a question about the reproducibility of

76

measurements as the tip changes. The durability of the tip will directly affect the cost for the

experiment and the performance of the tip will affect the accuracy of the measurements.

Therefore, the SEM process was added to check the tip before use.

The next discussion is comments on the roughness analysis. The thin film gold is the only

sample which showed surface features such as islands, resulting from the thin film deposition.

The mica was showed to be a flat surface, the reason could be the features are smaller than the

interference signal. From the average height, mica was shown to be the flattest surface. Further

investigation on the source of interference is more important, particularly for the harder

materials. When comparing the force measurements with roughness, it would also be possible

to set up an experiment of the same type of material with different roughness. The PTFE

showed the greatest variation in average height due to the very soft surface. The consequences

for the surface roughness will be considered for their impact on the thermal properties in the

next chapter.

The results in chapter 4.3 summarised the adhesive force measurements. The change in force

was described as adhesive force in this thesis because it is the amount of force on the surface

that attracts the tip. The difficulties of measuring the adhesive force when it reaches the limit

of the AFM was discussed. The method suggested in this thesis was to estimate the force by

fitting the intersection of two lines. However, this method has given an error on the estimated

force which is not usable, therefore the author attempted to adjust the range of force on the

AFM to avoid the situation and an unusual curve was observed showed in figure 4.12. The

unusual force curve shape was discussed and suggests that there may be a contamination layer

on the sample surface. This contamination layer was consistently detected on silicon, which an

extra layer of silicon oxide was expected on the silicon surface. A contamination layer also

consistently detected on PTFE while the PTFE consistently exhibited to the lowest adhesive

force.

77

To summarise, the force measurements in air are generally larger than in vacuum, this is due

to the layer of water formed on the surface which increases the adhesion. The adhesion can

vary across the surface, in the PTFE result the force curves were observed to have a step

variation across the area, which caused a large average height of 10 nm in roughness analysis.

The adhesion is particularly strong with silicon, but this was not always consistent. The silicon

showed an unusual shape of the force curve, which may be a result of an extra layer of different

material on the silicon surface i.e. silicon oxide. The adhesive force can be investigated from

the chemistry point of view, where the surface bonding and structure should be investigated

for a more comprehensive conclusion.

The samples in this experiment were chosen for their range of thermal conductivity. If further

mechanical analysis is required, the sample choice should add comparable samples, for

example the bulk gold and the thin film gold for direct comparison.

78

Chapter 5 SThM for thermal conductivity measurements

The aim for the thermal measurements is to first compare the thermal effects between air and

vacuum, since the environment can affect the heat path in SThM. The thermal measurements

will also be used to investigate how the mechanical properties affect the thermal results. The

thermal curves of the different samples will be compared and assessed for the feasibility of

making quantitative thermal transport measurements.

This chapter will present the following thermal measurements result. The signal from the data

logger and the thermal calibration will be presented, with a discussion on signal conversion

from voltage to temperature. The topography of each sample will be presented along with the

thermal map and the thermal curve in both vacuum and air. The comparison of the thermal

conductivity and the change in temperature for the different samples will be discussed and the

implications summarised.

5.1 Thermal calibration and probe signal from the data logger

Throughout the thermal experiment, the data logger is constantly monitoring the voltage across

the tip. The data logger is a useful part of the thermal measurements, it collects the temperature

information from the Peltier for thermal calibration. It is also used to alert the situation when

the probe circuit is being damaged during the experiment. The discussion starts with the

explanation of the data logger data. Figure 5.1 shows a typical result from the data logger for

thermal measurements.

79

a)

b)

Figure 5.1 a) A generic result of data logger recording in air. The diagram illustrates each part of the

curve during the experiment. From the beginning there is a potential difference drop for approach until

the tip is in contact with the surface. Then the potential difference remained during the topography

scanning. b) Continue the same diagram with labels of the measurement spikes, noise spikes and

indication of the data logger change in temperature. The measurement spikes are indicating the

temperature changes during the force and thermal measurements. The noise spikes are caused by the

40-second periodic instrumental noise. The data logger change in temperature indicates the

temperature difference between the tip in contact and out of contact of the sample.

80

At the beginning of the data logger recording, the tip is far away from the sample, then the

temperature drops during the approach process. It is noted in figure 5.1a that there is a steep

drop of the temperature during the approach process, this is because the specimen was

approached through a manual process. The distance of the probe and the specimen was

monitored by an optical microscope. Once the specimen is close enough that it cannot be

identified whether it is in contact, the AFM takes over for the fine approach.

When the temperature stops dropping, the tip is in contact with the sample. The tip would then

start scanning the topography of sample. Then the next step of the data logger curve shows the

probe temperature when the tip is measuring the force and thermal measurement. The force

and thermal results were repeated at 3 different points on the sample.

During the force or thermal single point measurements, the tip is programmed to approach and

retract to a pre-defined starting position, and reprogrammed to repeat. This is the procedure

that is programmed inside the AFM. It is obvious that when the tip is not in contact with the

sample, the tip temperature rises as there are fewer heat paths for the tip to cool down, this

causes the measurement spikes indicated in figure 5.1b. After all the measurements were made,

the tip retracts back to the starting position. The temperature would increase back to the value

when the tip is far away from the sample.

The data logger temperature measures the change in temperature between the tip in contact and

out of contact. An average of approximately 20 points were taken before the tip snap out and

after the tip snap out to the environment, the difference between the two values will be used as

the data logger temperature. This is used a reference temperature of heat loss to the environment.

81

The next discussion is the comparison of the data logger results between in air and in vacuum.

Figure 5.2 shows the data logger result of mica with 0.8mA current passing through the probe.

a)

b)

Figure 5.2 Data logger results of mica with 0.8mA in the environment of a) in air and b) in vacuum.

The results are comparing the measurement spikes height to the temperature when the tip is not in

contact in both environments.

The first characteristic is the change in temperature between the starting point and the contact

point, where we see that the overall temperature change in air is much higher than in vacuum.

By comparing the change in temperature measured in air and in vacuum, the temperature

change in vacuum is only about 10-20% of the temperature change in air, which supports the

theory discussed in chapter 2 where the air convection and solid-liquid conduction dominate

the thermal transport. The air conduction effect is also observed at the beginning. In figure 5.2a

there is a steep drop during manual approach, while in figure 5.2b the steep drop is not obvious.

82

This is because figure 5.2a the gas conduction is getting more effective when the tip gets closer

towards the sample, while in vacuum this effect is eliminated.

From both the data logger results in figure 5.2, the noise spikes showed an approximate 40

second periodic noise, the strength of the noise is approximately at 0.02V in air and 0.1V in

vacuum. This noise shows more obviously in vacuum than in air. From figure 5.2 the voltage

drop is about 0.7V while it is about 0.1V for in vacuum. Assuming the strength of the noise is

constant, the signal to noise ratio for air is larger than in vacuum, hence the noise is more

obvious in vacuum as the signal is lower. The source of the noise was not found during the

experiment, the possible reason is the internal electric interference caused by the computer.

The effect of the noise in temperature measurement will be discussed in the next section. The

thermal calibration is set up for measuring the change in temperature, it gives a conversion

from the change in voltage to change in temperature, it does not measure the absolute

temperature of the sample surface.

In air, the heights of the measurement spikes are significantly smaller compared to the data

logger change in temperature due to the heat loss by air. However, in vacuum there are only

radiation and solid-solid conduction for thermal transport, the heat loss due to air conduction

does not exist. Therefore the temperature does not vary with the tip-sample distance when they

are not in contact, hence the probe voltage retracts to its default value between each

measurement.

83

The next discussion is the data logger result of the thermal calibration. The data logger collected

the temperature of the Peltier and the tip current, the Peltier temperature was detected by a

PT100 thermometer. The data logger result plots the probe current and the Peltier temperature

against time. Figures 5.3 shows the data logger results during the calibration.

a)

b)

Figure 5.3 The data logger results of thermal calibration with the probe current of 0.8mA a) in air and

b) in vacuum.

The graph shows the tip current and the Peltier temperature, both plotted against time. The

calibration assumes the change in tip voltage and the change in Peltier temperature are linearly

proportional. The probe current will be plotted against the Peltier temperature which will be

used for converting voltage to temperature. Figure 5.4 illustrates the difference between the

two currents in the calibration.

25

30

35

40

45

50

55

60

4

4.5

5

5.5

6

6.5

7

7.5

8

8.5

9

200 300 400 500 600

Pe

ltie

r Te

mp

era

ture

(℃

)

Pro

be

Vo

ltag

e (

V)

Time (s)

Probe

Peltier

25

27

29

31

33

35

37

39

41

43

45

7.2

7.25

7.3

7.35

7.4

7.45

7.5

7.55

7.6

200 400 600 800

Tem

pe

ratu

re (

℃)

Pro

be

Vo

ltag

e (

V)

Time (s)

Probe

Peltier

84

a)

b)

Figure 5.4 Results of thermal calibration, graph of probe voltage against Peltier temperature

measured in a) air and b) vacuum.

Figures 5.4 shows the graph of probe current against the Peltier temperature in air and vacuum,

for each environment, two probe currents were used. The results that used 0.8mA were

observed to provide a larger gradient comparing to results that used 0.6mA. There are more

challenges in measuring the calibration in vacuum. The thermal transport in vacuum is limited

to two paths, so it takes longer for the probe to cool down than in air. The signal to noise ratio

is smaller in vacuum, and the temperature varies less than in air.

y = 0.1229x + 1.7608

y = 0.0783x + 1.057

4.5

5

5.5

6

6.5

7

7.5

8

8.5

9

25 30 35 40 45 50 55 60

Pro

be

Vo

ltag

e (

V)

Peltier Temperature (℃)

y = 0.006x + 7.1478

y = 0.0039x + 3.6211

3.5

3.6

3.7

3.8

3.9

4

4.1

4.2

4.3

4.4

4.5

7

7.05

7.1

7.15

7.2

7.25

7.3

7.35

7.4

7.45

30 35 40 45 50 55 60P

rob

e V

olt

age

(V)

of

0.6

mA

Pro

be

Vo

ltag

e(V

) o

f 0

.8m

A

Peltier Temperature(℃)

0.6mA

0.8mA

0.8mA

0.6mA

85

Figure 5.5 A graph of thermal calibration peak with both heating and cooling.

A hysteresis is observed in both air and vacuum environment, figure 5.5 shows this in air. The

opening of the loop shows a lag in temperature between the tip and the Peltier heater, caused

by the time delay on the temperature changes from the sample to the tip. Recalling figure 3.6

of the specimen photograph, the tip is measuring the calibration at the reserved space, which

took about half of the specimen size. Since the tip head is at a much smaller scale, there is a

significant distance on the specimen for the heat to transfer towards the thermometer, which

causes the hysteresis in the calibration.

When estimating the conversion gradient, the line of best fit for both heating and cooling curves

were fitted. In table 5.1 where the results are presented, only the cooling range was chosen for

the conversion. During the thermal measurement, the tip will be cooled down when it is in

contact with the sample, with this reason the cooling range of the calibration curve is better for

the behaviour of the tip.

5.3

5.8

6.3

6.8

7.3

7.8

8.3

30 35 40 45 50 55

Pro

be

Vo

ltag

e (V

)

Peltier Temperature (℃)

86

Probe

Coefficient of

conversion

(V/℃) %error

Operating

Current

(mA) Environment

Pressure

A 0.079±0.0004 0.24 0.6 In air atmospheric

B 0.0038±0.0003 0.81 0.6 In vacuum 2.0 × 10−4mbar

C

0.124±0.0003 0.30 0.8 In air atmospheric

0.0059±0.0002 0.92 0.8 In vacuum 1.7 × 10−4 mbar

Table 5.1 Table of the conversion coefficient of the thermal probes used in thermal measurements.

The calibration measurement is presented in table 5.1, including the thermal calibration of 3

thermal probes with different current passing through and in different environment. The

coefficient of conversion is the average gradient of the 3 repeated peaks measured in the

calibration and the error is estimated as the standard deviation of the repeated value. The

pressure for when the calibration measured in vacuum is also noted in the table.

For thermal probe B, the probe was heated to 60 degrees and allowed to cool down naturally

with the current at 0.6mA. There was a thermal jump observed in this measurements, the

method was showed in chapter 3. The method used in thermal probe C was optimised based on

the result of thermal probe B. The result for thermal probe C presented in Table 5.1 is using

the 40-degree method, where the probe was heated to 40 ℃ and cooled down naturally.

The author used the air calibration coefficient for converting both vacuum and air thermal

measurements. The tip temperature was assumed to be the same as the sample in air, however

this assumption does not hold in vacuum. As a result, the calibration coefficient in vacuum is

extremely low and the change in temperature signal in vacuum is smaller than in air. From

table 5.1, the thermal calibration gradient measured for vacuum is significantly smaller than

that measured in air. For example, for probe C, the air coefficient is 0.12 V/℃, this is about 20

times larger than the coefficient measured in vacuum. The vacuum change in temperature

voltage signal is small because of the lack of heat paths, when the extremely low calibration

87

coefficient is used to convert to temperature, it would result in an overestimation of the sample

temperature change. Therefore, in the following chapters, the thermal measurement units are

converted using only the air calibration respects to the probe.

88

5.2 Thermal map and the thermal measurements

This section will present the thermal measurement results for each sample measured in air and

vacuum. The section will start with the discussion on the characteristics of the thermal maps

and the thermal curve. The results will then be presented, starting with presenting the results in

air, then move onto vacuum.

The thermal map was generated by feeding the thermal signal into the force section of the

feedback module as shown in figure 3.4. The processing software WSxM registered the signal

as a standard force signal and automatically programmed the conversion into picometer. The

conversion from picometer to volts is noted and will be provided along with all the thermal

maps in this project.

Figure 5.6 a) The unprocessed thermal map of SiC in air b) the processed thermal map of SiC in air.

For both figures the conversion 10.02pm/V.

In the chapter 5.1, when introducing the 40 second noise from the data logger, it was shown

that there were temperature spikes with a period of approximately 40 seconds. This noise

affects the thermal map that is collected during the topography measurements. In figure 5.6a,

the dark lines in the thermal map are the periodic noise from the instrument. Various possible

origins of this noise were investigated including the tip and the connection between data logger

and the SThM, however the source was not identified. After the change of tips, the noise still

100nm

60.12 pm

0.00 pm

100nm

17.49 pm

0.00 pm

89

appeared in all the results. The noise was removed in the WSxM software, the flatten process

in the software was used to eliminate the line of noise and the contrast of the image was adjusted.

The temperature measurements were made away from these areas.

In the following presentations, the thermal maps were processed in the WSxM software, figure

5.6b) shows an example of the thermal map after repairing in WSxM. The scale bar of the

thermal maps will be presented in pm, along with a conversion from pm to V given by the

WSxM software. The thermal measurements are designed to measure the change in

temperature, the thermal calibration presented only allows the conversion of the change in tip

voltage V to the change in temperature ℃. The scale bar effectively shows the total change in

temperature ℃ of the thermal map, however, this total change in temperature is different from

the data logger temperature change. The reason is the probe current is calibrated before the

experiment, the voltage across the tip is offset from the real voltage, therefore the temperature

results of the thermal map and the data logger are not comparable.

Figure 5.7 Thermal curve of PTFE measured in vacuum. The thermal curve presented is an average of

9 curves. The step jump is caused by different responses at each area.

90

The thermal curves presented are an average of all 9 curves measured on each sample. The step

jump noted in figure 5.7 is caused by the different response between each area on the same

sample. Figure 5.8 is showing the individual curve of each area.

Figure 5.8 Thermal curve of PTFE at 3 different areas measured in vacuum.

The reason causing the step jump in figure 5.7 is the curve was averaging the 9 measurements

made in all areas, when the tip doesn’t snap out from the same point from the sample, this will

generate a variation between the areas. This variation is demonstrated in figure 5.8 showing a

comparison of the thermal curves measured in three different areas. This happens more often

for a soft material such as PTFE, this is because the tip deforms the material surface and can

affect the adhesive force. The approach temperature will be used to compare the samples in

this section and with thermal conductivity in section 5.3.

6.94

6.96

6.98

7

7.02

7.04

7.06

7.08

-400 -200 0 200 400 600 800 1000

Tem

pe

rtu

re (

V)

Displacement (nm)

Area 1

Area 2

Area 3

91

a)

b)

Figure 5.9 The thermal curves of a) PTFE and b) SiC measured in air.

The comparison of the thermal curves between materials within the same environment will be

discussed in this section. Figure 5.9 shows the comparison of the thermal curve shapes between

the PTFE and SiC within the same environment. After the tip is in contact with the material,

the soft material showed a further decrease in temperature compared to the harder material, this

is marked in figure 5.9a. This is because after the tip is in contact, the SThM will keep

approaching until it reaches the pre-set distance. Since the tip is harder than the PTFE, the tip

will deform the PTFE surface and create more contact area for the heat to transport, hence the

further drop with temperature.

5.24

5.26

5.28

5.30

5.32

5.34

5.36

5.38

5.40

5.42

5.44

-500 0 500 1000 1500 2000

Tem

per

atu

ire

(V)

Displacement (nm)

92

The next section will present the thermal results measured with the probe current of 0.8mA as

the tips were broken during the measurements using 0.6mA resulting in a change of tip. The

results between the two probes cannot be directly compared without taking into account the

difference of the tip. For example, the tip contact area could be different, which adds another

systematic error. However, the 0.6mA results can still be compared within the set.

The order of presenting each material is the same as the topography results in the previous

chapter. The presentation of figures 5.10 to 5.14 will come in the following sequence from the

left: topography marked with the points where thermal measurements were made, the thermal

image on the right that is along with the topography and then an average thermal curve of the

thermal measurements at the bottom with the corresponding force curve. The thermal curve is

obtained by averaging the curves measured at 3 areas, and at each area the curve is repeated 3

times. The resulting curve shows the average of total 9 curves from one sample. The conversion

values are presented at the bottom of the figures.

At the end of the graphical presentation of the thermal maps, a table of the thermal

measurement results will be presented for each environment. The table will include the

approach, retract and the data logger change in temperatures.

A general discussion on the values within the environment will be discussed with the table. At

the end of the chapter, both numerical results will be combined and compared with further

discussion. The interpretation and further analysis of the data will be presented in chapter 5.4

93

Thermal map scale bar

conversions

pm to V: 38.3 pm/V

pm to ℃: 4.73 pm/℃

Figure 5.10 The results for gold thin film in air.

Thermal map scale bar

conversions

pm to V: 8.85 pm/V

pm to ℃: 1.09 pm/℃

Figure 5.11 Thermal results of Mica in air.

7.90 nm

0.00 nm

100nm

15.80 pm

0.00 pm

5.2

5.22

5.24

5.26

5.28

5.3

5.32

5.34

5.36

5.38

-200

-100

0

100

200

300

400

-500 0 500 1000 1500 2000

Tem

pe

ratu

re (

V)

Forc

e (

nN

)

Displacement (nm)

Force curve

Thermal curve

1.85 nm

0.00 nm

100nm

13.07 pm

0.00 pm

5.26

5.28

5.3

5.32

5.34

5.36

5.38

5.4

5.42

5.44

-200

-100

0

100

200

300

400

-500 0 500 1000 1500 2000

Tem

pe

ratu

re (

V)

Forc

e (

nN

)

Displacement (nm)

Force curve

Thermal curve

94

Thermal map scale bar

conversions

pm to V: 11.8 pm/V,

pm to ℃: 1.46 pm/℃

Figure 5.12 Thermal results of PTFE in air.

Thermal map scale

bar conversions

pm to V: 8.85 pm/V

pm to ℃: 1.09 pm/℃

Figure 5.13 Thermal results of Silicon in air.

24.53 nm

0.00 nm

100nm

14.40 pm

0.00 pm

4.96

4.98

5

5.02

5.04

5.06

5.08

5.1

-100

0

100

200

300

400

500

-500 0 500 1000 1500 2000

Tem

pe

ratu

re (

V)

Forc

e (

nN

)

Displacement (nm)

Force curve

Thermal curve

5.79 nm

-0.01 nm

100nm

13.43 pm

0.00 pm

5.32

5.34

5.36

5.38

5.4

5.42

5.44

5.46

5.48

5.5

-300

-200

-100

0

100

200

300

400

500

-1000 -500 0 500 1000 1500 2000 Tem

pe

ratu

re (

V)

Forc

e (

nN

)

Displacement (nm)

Force curve

Thermal curve

95

Thermal map scale bar

conversions

pm to V: 10.02 pm/V

pm to ℃: 1.23 pm/℃

Figure 5.14 The results of silicon carbide in air.

The first discussion would be the comparison of the thermal map and the thermal curves. The

first result presented was the thin film gold, the sample with an unknown thermal conductivity.

The hardness of the material was expected to be softer than Silicon but harder than mica

because of the bulk elastic modulus value of gold. The topography shows that there are some

surface features. The thermal curve shows that there is a slight deformation after the tip contacts

with Au as the temperature dropped after the tip is in contact.

In the previous chapter, the mica did not show any features on the topography, the thermal map

supports this observation by having a low contrast image. The thermal map is picking up a

strong interference signal and the surface structure did not show on the thermal image. The

possible reason is the effect of the mica surface features were smaller than the interference

signal, so only the interference was measured. The thermal curve shows some temperature drop

after the contact point.

16.72 nm

0.00 nm

100nm

11.80 pm

0.00 pm

5.24

5.26

5.28

5.3

5.32

5.34

5.36

5.38

5.4

5.42

5.44

-200

-150

-100

-50

0

50

100

150

200

250

300

350

-500 0 500 1000 1500 2000 Tem

pe

ratu

re (

V)

Forc

e (

nN

)

Displacement (nm)

Force curve

Thermal curve

96

The PTFE showed some features on the topography. The thermal curve shows that there is a

clear gradient drop after the tip approached the surface as described earlier in this section. The

thermal curve in figure 5.12 shows the step change at the retract temperature path that was

described in figure 5.7. This is due to the soft surface of PTFE that causes different responses

between each area.

The thermal image of silicon is similar to mica, a strong interference signal was collected and

affects the clarity of the thermal map. Although the silicon thermal image showed some surface

features, the noise signal is very similar to mica. The thermal curve shows a clear change in

temperature for approach and retract.

Silicon carbide is the hardest material in the sample set, the topography and thermal map both

collected the interference signal. Some features on the topography can be seen on the thermal

map. The change in temperature was expected to be the largest due to the highest thermal

conductivity from the set, however the temperature change is smaller than Si.

97

Table 5.2 presents the change in temperature measured in air. The table is arranged with a

descending order of thermal conductivity. The thin film gold was arranged at the bottom of the

table because it is the sample with unknown thermal conductivity.

Environment

Material

Thermal

Conductivity

(W/m⋅K)

dT

(approach) (℃) %error

dT

(retract) (℃) %error

dT

Data logger (℃) %error

In Air

with

atmospher

ic

pressure

SiC 420 0.35±0.01 2.6 0.48±0.05 1.0 5.80±0.07 1.2

Si 124 0.388±0.004 0.9 0.69±0.01 1.1 5.68±0.08 1.4

Mica 0.53 0.26±0.01 3.7 0.41±0.01 2.4 5.51±0.08 1.3

PTFE 0.2 0.14±0.02 11 0.23±0.01 3.3 4.43±0.09 1.9

Au 314(bulk) 0.24±0.02 6.8 0.44±0.02 4.5 5.90±0.08 1.3

Table 5.2 Table of temperature measurements from the thermal probe in air, with a current of 0.8mA.

The first observation is comparing the numerical results from the different parts of the

measurement to verify the characteristics of the thermal measurements as discussed in chapter

2. The change in temperature recorded by the data logger is higher than the retract or the

approach value in air. This is because the tip was approaching from far away and heated. As

the distance between the sample and the tip gets closer, the air conduction and convection effect

will increase and the tip will cool down. The approach temperature values are smaller than the

retract temperature in general, this is because the air conduction dominated the temperature

measurements, as described in chapter 2. When comparing the retract and approach value, the

approach value is more important for interpretation with the thermal conductivity. The reason

is that there is no extra force such as the adhesive force measured in the previous chapter to

affect the contact with the sample.

The approach temperature for all samples showed three different categories of temperature

change, the silicon and silicon carbide at the highest end of the temperature table; the mica and

thin film gold at the middle; and the PTFE being the lowest of the table. When comparing the

three categories with the thermal conductivity, the first observation is the sample with larger

98

change in temperature would have higher thermal conductivity. The PTFE has the lowest

thermal conductivity and change in temperature.

The silicon has a higher value of approach temperature than the silicon carbide. The error for

silicon is small, which indicates that the results are consistent. Recalling the results from

chapter 4, the silicon also has the largest adhesive force value, however the adhesive force

measurements only affect the retract temperature. The possible explanation for this is whether

the silicon carbide change in temperature was lower than expected, or the silicon value being

higher than expected.

Comparing the mica result to silicon carbide and silicon, the approach temperature of mica was

consistently significantly lower than silicon carbide. The explanation follows the same

argument of thermal conductivity of the materials. This indicates that the silicon is showing a

higher value than expected.

The thin film gold approach temperature is observed to be smaller than mica. The thermal

conductivity of thin film gold was expected to be similar to bulk gold material. However, the

observation indicated the thin film gold had as similar value of thermal conductivity to mica.

99

Figure 5.15 to 5.19 will continue presenting the graphical measurements for each sample, the

results were measured in vacuum. The presentation of the figures will continue with the

previous sequence. The vacuum pressure was measured at 1.7 × 10−4 mbar and the probe

current was the same at 0.8mA. Table 5.3 summarises the change in temperature and the

comparison will be discussed after the graphical results in table 5.4.

Thermal map scale bar

conversions

pm to V: 38.6 pm/V

pm to ℃: 4.76 pm/℃

Figure 5.15 Thermal results of thin film gold in vacuum.

18.89 nm

0.00 nm

65.82 pm

0.00 pm

6.84

6.86

6.88

6.9

6.92

6.94

6.96

6.98

7

-150

-100

-50

0

50

100

150

-400 -200 0 200 400 600 800 1000Te

mp

era

ture

(V

)

Forc

e (

nN

)

Displacement (nm)

Force curve

Thermal curve

100

Thermal map scale bar

conversions

pm to V: 17.3 pm/V

pm to ℃: 2.14 pm/℃

Figure 5.16 Thermal results of Mica in vacuum.

Thermal map scale bar

conversions

pm to V: 20.9 pm/V,

pm to ℃: 2.58 pm/℃

Figure 5.17 Thermal results of PTFE in vacuum.

2.20 nm

0.00 nm

100nm

10.38 pm

0.00 pm

5.1

5.12

5.14

5.16

5.18

5.2

-150

-100

-50

0

50

100

150

-400 -200 0 200 400 600 800 1000

Tem

pe

ratu

re (

V)

Forc

e (

nN

)

Displacement (nm)

Force curve

Thermal curve

28.72 nm

0.00 nm

100nm

50.80 pm

0.00 pm

6.94

6.96

6.98

7

7.02

7.04

7.06

7.08

-150

-100

-50

0

50

100

150

200

250

300

-400 -200 0 200 400 600 800 1000

Tem

pe

ratu

re (

V)

Forc

e (

nN

)

Displacement (nm)

Force curve

Thermal curve

101

Thermal map scale bar

conversions

pm to V: 16.2 pm/V

pm to ℃: 2.00 pm/℃

Figure 5.18 Thermal results of silicon in vacuum.

Thermal map scale bar

conversions

pm to V: 23.4 pm/V

pm to ℃: 2.89 pm/℃

Figure 5.19 Thermal results of silicon carbide in vacuum.

12.15 nm

0.00 nm

100nm

10.23 pm

0.00 pm

6.8

6.85

6.9

6.95

7

7.05

-150

-100

-50

0

50

100

150

200

250

300

-400 -200 0 200 400 600 800 1000

Tem

pe

ratu

re (

V)

Forc

e (

nN

)

Displacement (nm)

Force curve

Thermal curve

4.84 nm

0.00 nm

100nm

26.39 pm

0.00 pm

6.68

6.7

6.72

6.74

6.76

6.78

6.8

6.82

6.84

6.86

-100

-50

0

50

100

150

-400 -200 0 200 400 600 800 1000 Tem

pe

ratu

re (

V)

Forc

e (

nN

)

Displacement (nm)

Force curve

Thermal curve

102

The thin film gold showed some patterned island features on the topography, this is consistent

with the results in air. Although the thin film gold does not have a dedicated fabrication pattern,

the topography shows the surface structural difference between the thin film sample and bulk

samples. There is a small temperature variation before the tip snaps out the surface, this is

consistently showing in all 9 points measured on the gold sample. The reason for this is not

known and it has not been investigated.

For mica, the topography result has shown a clearer result in air. The interference noise was

not significant enough to interfere the surface features on the topography results. A clear

change in temperature is shown in the thermal curve and is synchronised with the force curve.

The topography of PTFE showed the same feature characteristic as the result in air. The thermal

curve shows more clearly the variation between areas, the step jump at the retract area was

noted and discussed in the earlier of this section.

The topography of silicon in vacuum has the same characteristic as measured in air, the thermal

map showed the strong interference. The thermal curve shows the biggest temperature drop

from the sample set measured in vacuum, the force curve verified the position of where the

probe snapped in and snapped out. This has the same characteristic as the results from air.

The thermal map of silicon carbide collected the interference at the top of the map. The

interference signal was hugely reduced during the measurement. The cause of it is not known.

The features on the silicon carbide also showed on the thermal map.

103

Environment

Material

Thermal

Conductivity

(W/m⋅K)

dT

(approach)

(℃) %error

dT

(retract) (℃) %error

dT

Data logger

(℃) %error

In Vacuum

Pressure: 1.7 ×

10−4 mbar

SiC 420 1.03±0.01 1.3 0.95±0.02 2.6 1.19±0.02 1.0

Si 124 1.48±0.01 0.33 1.29±0.01 0.88 1.52±0.03 2.3

Mica 0.53 0.82±0.01 1.4 0.80±0.01 1.7 0.83±0.03 3.6

PTFE 0.2 0.68±0.02 2.3 0.58±0.05 9.4 0.90±0.01 1.1

Au 314(bulk) 0.76±0.04 5.9 0.90±0.03 2.6 1.07±0.03 3.2

Table 5.3 Table of temperature measurements from the thermal probe in vacuum, with a current of

0.8mA.

Table 5.3 shows the vacuum temperature results arranged in the descending order of thermal

conductivity. The first observation is that the data logger change in temperature is similar to

both the approach and the retract temperature, unlike the big difference observed in air. This is

because there was no air conduction in vacuum, the gas cooling dependence on the tip-sample

distance is eliminated, hence the variation of the change in temperature is small. With the same

reason, the approach and retract values are also similar. The approach temperature in vacuum

generally follows the same order of thermal conductivity.

The first comparison is to compare the silicon and silicon carbide approach temperature. The

silicon approach temperature is larger than silicon carbide, which is consistent with the results

in air. The same occurs with the retract temperature. The error for both samples are small and

the results are consistent. The silicon carbide approach temperature is larger than mica, which

is consistent with the expected result.

The mica approach temperature follows the same observation as in air, where the change in

temperature is larger than gold. When comparing the retract temperature to the approach

temperature, both temperature measurements are the same for mica.

The change in temperature for PTFE is the smallest, the result is expected as the PTFE has the

smallest thermal conductivity from the sample set. The PTFE has the soft surface and the error

is expected to be large. However, from the figure 5.8 the variation of the approach temperature

104

was not so large. The PTFE error result showed that the retract value has greater percentage

error of 9.4% than the approach error of 2.3%.

For the measurements of gold, the temperature value is similar to mica for both approach and

retract. The gold approach temperature is smaller than mica in vacuum, however the difference

is small. This observation supports the deduction of the gold sharing the similar range of

thermal conductivity with mica. However, the error for approach temperature is big, this is

because the gold did not show a clear drop on the thermal curve, this causes a large variation

when taking the measurements. The gold surface has a high variation across the area that is

similar to PTFE described in figure 5.8. This variation is also causing difficulties on making

the measurements, hence the 5.9% error on approach value.

105

Table 5.4 will compare the temperature measurements of each sample in the two environments.

The characteristic of each environment was discussed individually in the above section. The

conversion coefficient used the measured value in air of 0.12 V/℃.

Environment

Material

Thermal

Conductivity

(W/m⋅K)

dT

(approach)

(℃) %error

dT

(retract) (℃) %error

dT

Data logger

(℃) %error

In Air with

atmospheric

pressure

SiC 420 0.35±0.01 2.6 0.48±0.05 1.0 5.80±0.07 1.2

Si 124 0.388±0.004 0.9 0.69±0.01 1.1 5.68±0.08 1.4

Mica 0.53 0.26±0.01 3.7 0.41±0.01 2.4 5.51±0.08 1.3

PTFE 0.2 0.140±0.02 11 0.23±0.01 3.3 4.43±0.09 1.9

Au 314(bulk) 0.24±0.02 6.8 0.44±0.02 4.5 5.90±0.08 1.3

In Vacuum

Pressure:

1.7 × 10−4

mbar

SiC 420 1.03±0.01 1.3 0.95±0.02 2.6 1.19±0.02 1.0

Si 124 1.48±0.01 0.33 1.29±0.01 0.88 1.52±0.03 2.3

Mica 0.53 0.82±0.01 1.4 0.80±0.01 1.7 0.83±0.03 3.6

PTFE 0.2 0.68±0.02 2.3 0.58±0.05 9.4 0.90±0.01 1.1

Au 314(bulk) 0.76±0.04 5.9 0.90±0.03 2.6 1.07±0.03 3.2

Table 5.4 Table of temperature measurements from thermal probe, measured in 0.8mA.

When comparing the numerical results from the different environments, the first observation

is the change in data logger temperature is about 5 times larger than in vacuum. The data logger

result measures the heat loss from far away of the sample to after the tip approaches. In the air

case, when the tip is far away from the sample, the tip loses heat to the air hence the change in

temperature is larger in air. In vacuum, the air was eliminated, when the tip is far away from

the sample, the tip temperature loss by the thermal radiation is negligible and could not be

measured. This can be showed by the change in temperature are similar between approach,

retract and the data logger.

The results show that the vacuum change in temperature is generally larger, for both approach

or retract. In air, the tip is cooling as it approaches to the sample, when it snaps in, the

temperature difference between the tip and the sample has greatly reduced. In vacuum, the

106

temperature was not cooled by the air conduction, when the tip snaps in, the change in

temperature is then larger. Although there is a much smaller contact area in vacuum, the signal

is larger.

From both environments, the gold results are similar to mica. In both cases, the approach

temperature of gold is larger than mica. The retract temperature and the data logger results are

smaller, however, the retract values are less reliable as described in chapter 2. Therefore,

judging by the approach temperature, the gold thin film is expected to have similar thermal

conductivity to mica.

The error presented in the table is the variation of the measurements taken at all the 9 areas, it

was calculated using the standard deviation of the repeated values. The error for retract values

was expected to be larger in air than the approach values because the snap out point is not

repeatable. However, the variation was not big and the error is similar for both attract and

retract.

The error analysis for this section only discusses the numerical error that was able to be

measured during the measurements. However, there are more factors that could affect the

numerical results. During the experiment in both environments the pressure and the humidity

were not controlled, this could affect the amount of water forming on the sample surface. The

hysteresis effect described in figure 5.5 was noted as an error when measuring the thermal

calibration. This effect was not taken into account when calculating the change in temperature.

However, since all of the temperatures were converted through the same calibration coefficient

and only the change in temperature was measured, the contribution of this error would be the

same for all thermal values.

107

The thermal calibration was performed before the thermal readings were taken with the samples

on the heater during the calibration process. This causes the samples to be heated at a certain

temperature and then cooled down while the thermal measurements were being taken. Figure

5.20 presents the data logger result of silicon, which was the first sample being measured in

the data set.

Figure 5.20 The data logger results of silicon in air showing the sample cooling during the

experiment.

In figure 5.20, after the tip snapped in, the temperature voltage dropped to about 5.4V and by

the end of the experiment, the temperature has dropped to approximately 5.3V. This shows

that the sample was cooling during the measurements and might result in dT being smaller

than expected. However, as the data presented were collected towards the end of the

measurement, the temperature difference was expected to be small.

108

5.3 Discussion and interpretation of thermal measurements and

thermal conductivity

In section 5.2, the graphical results measured in both air and vacuum were presented, the

general observations and the comparison were discussed according to the environment. The

numerical result of approach, retract and the data logger change in temperature were compared

for both environments.

This section will continue the analysis of the thermal data, the analysis will discuss the

interpretation of the physics from the results of both chapters 4 and 5 as presented in the

summary table 5.5.

109

E

nv

iro

nm

ent

Mat

eria

l

Ther

mal

Conduct

ivit

y

(W/m

⋅K)

Ela

stic

modulu

s

(GP

a)

dF

(ret

ract

)

(nN

) dT

(appro

ach)

(℃)

dT

(ret

ract

)

(℃)

dT

Dat

a

logger

(℃)

Def

orm

atio

n

(℃)

Def

orm

atio

n

to

dT

(appro

ach)

%

Per

centa

ge

hea

t lo

ss

(%)

In

Air

w

ith

atm

osp

her

ic

pre

ssure

SiC

420

302

175±

1.9

6

0.3

5±

0.0

1

0.4

8±

0.0

5

5.8

0±

0.0

7

0.1

07±

0.0

01

31

94

Si

124

179

179±

1.6

0.3

88±

0.0

04

0.6

9±

0.0

1

5.6

8±

0.0

8

0.1

19±

0.0

01

31

93

Mic

a 0.5

3

170

165±

0.3

0.2

6±

0.0

1

0.4

1±

0.0

1

5.5

1±

0.0

8

0.1

03±

0.0

02

39

95

PT

FE

0.2

0

.4

77±

1.1

0.1

40±

0.0

2

0.2

3±

0.0

1

4.4

3±

0.0

9

0.1

66±

0.0

03

119

96

Au

314(b

ulk

) 7

9(b

ulk

) 144±

0.5

4

0.2

4±

0.0

2

0.4

4±

0.0

2

5.9

0±

0.0

8

0.1

80±

0.0

05

75

97

In V

acuum

Pre

ssu

re:

1.7

×1

0−

4

mbar

SiC

420

302

133±

5.2

1.0

3±

0.0

13

0.9

5±

0.0

2

1.1

9±

0.0

2

0.1

39±

0.0

03

13

13

Si

124

179

153±

5.8

1.4

8±

0.0

05

1.2

9±

0.0

1

1.5

2±

0.0

3

0.1

18

±0

.00

1

7.9

2.7

Mic

a 0.5

3

170

144±

3.2

0.8

2±

0.0

12

0.8

0±

0.0

1

0.8

3±

0.0

3

0.0

90±

0.0

01

11

1.1

PT

FE

0.2

0

.4

160±

3.9

0.6

8±

0.0

15

0.5

8±

0.0

5

0.9

0±

0.0

1

0.1

57±

0.0

03

23

9.8

Au

314(b

ulk

) 7

9(b

ulk

) 145±

9.7

0.7

6±

0.0

4

0.9

0±

0.0

3

1.0

7±

0.0

3

0.2

99±

0.0

09

39

24

Ta

ble

5.5

. A

sum

ma

ry t

ab

le f

or

ove

rall

the

data

. T

he

table

show

ed t

he

mate

rial,

the

ther

mal

conduct

ivit

y, t

he

ela

stic

mo

dulu

s, t

he

retr

act

fo

rce,

th

e ch

an

ge

in

tem

per

atu

re f

or

app

roach

, re

tra

ct a

nd

fo

r th

e da

ta l

ogger

. T

he

new

ele

men

ts a

re t

he

def

orm

ati

on c

olu

mn, w

her

e m

easu

rin

g t

he

tem

per

atu

re d

rop

ped

aft

er t

he

tip

def

orm

s th

e sa

mple

. T

he

per

centa

ge

hea

t lo

ss i

s ca

lcula

ting

the

per

centa

ge

rati

o o

f a

ppro

ach

to

data

lo

gger

.

110

The table 5.5 summarised the results in section 5.2, the extra columns are attempts to analyse

the change in temperature with surface hardness, the deformation temperature, and with the

environment the percentage heat loss.

The first discussion will be the deformation temperature. The deformation temperature is the

temperature change detected while the tip is in contact with the samples. The deformation is

taking the difference of Vmin used for measuring the approach temperature and the Vdeform at

the contact region. The difference of this value was divided by the approach temperature and

converted to a percentage. The range of values are illustrated in figure 5.21.

Figure 5.21 Result of PTFE illustrating the method of calculating deformation temperature changes.

For the soft samples, the deformation temperature is expected to be larger than hard materials.

This is because when the tip is in contact with the sample, the tip is pushing towards the sample

surface, which for soft materials would increase the contact area for mechanical conduction

and solid liquid conduction. However, the tip might also deform while in contact with a hard

material.

111

In the air result, the deformation for PTFE is significantly larger than other samples. The harder

materials such as silicon and silicon carbide are similar with 31%. The thin film gold showed

a high percentage deformation of 75%. In vacuum, the samples showed a different trend with

air. The gold was observed have a larger deformation temperature than PTFE. The possible

explanation is in vacuum, the elimination of gas conduction and solid liquid conduction

affected the trend observed in air. Since the thermal conduction is depending on the thermal

conductivity of the material and the gold was expected to have a higher thermal conductivity

than PTFE, the deformation results are then explained. The tip deformation of gold provides

evidence that the gold thin film is a soft material.

The next discussion will be the percentage heat loss, this calculation is an attempt to find out

the amount of heat loss due to the environment. For the calculation, the data logger change in

temperature was used to be the overall temperature change. The approach temperature was

used as the heat transported between the tip and the sample, also the approach temperature is

more reproducible. The heat loss by the environment is calculated by the difference between

the data logger temperature and approach temperature, then converted into percentage of the

data logger value. From the result in air, the percentage heat loss is generally above 90%. In

vacuum, the heat loss is expected to be lower than in air, the average heat loss from the data is

approximately 10%.

The following part will present the thermal measurements against the thermal conductivity and

discuss the method to determine the unknown conductivity of a sample. Throughout the chapter

4 and 5, the properties of gold thin film were not known. From both force and thermal results,

there is evidence that the gold thin film would have a similar hardness and thermal conductivity

with mica, this is shown by similarity of the two sample values measured in the previous

sections.

112

In order to determine the thermal conductivity of gold, the relationship between the approach

temperature and the sample thermal conductivity would first need to be investigated. The

approach temperature measurements are the important values used to determine the

relationship with the thermal conductivity. The reason is the approach temperature has a

consistent snap in point that is reproducible. The approach temperature is plotted against the

thermal conductivity in figure 5.22.

Figure 5.22 The approach temperature change against the thermal conductivity.

Figure 5.22 shows all samples in all environments at different probe currents, without the gold

values. The first observation is that with the same current, the vacuum measurements are

consistently larger than in air. The results in figure 5.22 was measured with three different tips

(A, B and C as described in chapter 4). For the results of 0.6mA, the measurements in air and

vacuum were using two different tips. The different tips could have different contact areas and

can cause an inconsistency, therefore the data with the same probe current was only used to

compare within the set. The data of 0.8mA was using the same tip, and so the results can be

compared with different environments.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

-50 50 150 250 350 450

dT

(ap

pro

ach

) (℃

)

Thermal Conductivity (W/m.K)

0.8mA, vacuum

0.6mA, vacuum

0.8mA, air

0.6mA, air

113

The silicon has an inconsistent result shown in figure 5.22. From the 0.8mA result, the silicon

shows an approach temperature larger than the silicon carbide, while for 0.6mA the result is

vice versa. There may have been surface changes to the sample or the tip. Although it is also

the case that when the thermal sensitivity of the tip is similar to the sample, the tip reaches a

limit on measuring the change in temperature. [12] The shape of the curve showed that there is

a limit towards the higher thermal conductivity. Since the range of thermal conductivity is large,

in order to compare mica and PTFE, the graph was replotted with a smaller horizontal.

Figure 5.23 shows the range of thermal conductivity for the samples with a smaller thermal

conductivity, the vacuum results remained consistently larger than air.

Figure 5.23 The approach temperature change against the thermal conductivity for small thermal

conductivity. The gold is shown as a horizontal line as the thermal conductivity is not known.

The PTFE change in temperature is smaller than mica in all environments. The error in figure

5.23 shows more clearly than in figure 5.22, since the standard deviation of the samples are

small in figure 5.22 the error bars are negligible. However, there are some inconsistencies from

the gold and silicon result that are noticeable. Therefore, the reproducibility of the

measurements is much poorer than the standard deviation is implying.

114

Figure 5.24 The approach temperature change against the thermal conductivity for small thermal

conductivity. The silicon values have plotted with the silicon oxide thermal conductivity of 1.1 W/m⋅K.

Figure 5.24 has an additional point from figure 5.23, it has the silicon plotted with the silicon

oxide thermal conductivity of 1.1 W/m⋅K. The reason is since the silicon is known to have a

layer of silicon oxide on the surface, the heat transfer could be from the tip to the silicon oxide

and the silicon change in temperature could be different from the measured value. With the

silicon oxide thermal conductivity, the change in temperature was observed to have a better

linear correlation with the lower range of thermal conductivity. However, the silicon oxide and

silicon samples would need to be modelled and compared for a more conclusive deduction.

The discussion is now the thermal conductivity of the thin film gold. The gold thin film is

believed to have a similar thermal conductivity as mica, since the mechanical and thermal

results were similar. In the previous discussion on the tip sensitivity, the tip becomes less

thermally sensitive when the thermal conductivity of the sample is comparable to the tip,

however with low thermal conductivity materials, the temperature drop is dependent on the

thermal conductivity.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.5 1 1.5

dT

(ap

pro

ach

) (℃

)

Thermal Conductivity (W/m.K)

0.8mA, vacuum

0.6mA, vacuum

0.8mA, air

0.6mA, air

Au, 0.8mA,vacuumAu, 0.6mA,vacuum

115

The thermal conductivity of the thin film gold is estimated by comparing the percentage

difference of the change in temperature with the thermal conductivity of mica. The gold change

in temperature was first calculated as a percentage range of mica, which gives a 16% difference.

The gold thin film thermal conductivity is estimated at the range of 0.44 – 0.62 W/ m⋅K,

compared to the bulk material of 314 W/ m⋅K. The thin film value was expected to be much

smaller than the bulk material due to the geometric constraints. [1] The thermal conductivity

estimation of this gold thin film sample is likely to be due in part to its structure and surface,

for example, the size of surface features, the thickness and roughness. Further investigation on

thin film samples would require modelling layers of different materials, in this gold thin film

example, the layer of silicon oxide on the silicon base and the chromium adhesive should also

be modelled.

116

Chapter 6 Conclusions and further developments

This chapter will summarise the work completed, the results achieved and suggest future

developments for this project.

Different methods for measuring the spring constant of the AFM cantilever were considered

and the SEM method chosen and used due to its practicality. The spring constant for the thermal

tips has successfully been measured as a range of 0.5 – 2.6 N/m and the contact tip spring

constant has been measured as 23.1 N/m. The spring constant of the contact tip has been shown

to have a much higher spring constant than the thermal tip. The spring constant has been used

in converting deflection to force units. One challenge for this is there are impurities on the

cantilever, for which the effect on the spring constant is unknown. The Young’s modulus was

estimated as that of silicon nitride, as the structure of the probes gets more complex, the

Young’s modulus can directly affect the spring constant calculated. The thermal resistor was

found to be peeling off from the tip after an experiment. Hence the tip verification using SEM

was added as a standard procedure before thermal experiments.

The methodology of force and thermal measurements were presented in Part II of chapter 3.

The topography, force and thermal measurements for each sample were presented in Chapter

4 and Chapter 5. For some samples having a high adhesive force such as silicon, the AFM

reached a limit regardless of the measurement environment. A method for obtaining the

adhesive force from this data was suggested using a line of best fit of the data, which inevitably

introduced an additional error. Some force curves also could not be fitted with a straight line,

due to deformation of the surface. The other method suggest was offsetting the range on the

AFM, this then revealed a force curve with an unusual shape which it is thought is caused by

a surface layer, which could be contamination, or an instrumental effect.

117

A method of thermal calibration of the thermal tips was presented. The data logger was used

to monitor the potential of the tip and the temperature signal from the PT100 thermometer. For

the thermal calibration, a hysteresis was observed between the heating and the cooling in both

air and vacuum. Various calibration methods were attempted for vacuum however, the

conversion coefficient was shown to be 20 times smaller than calibration in air due to the poorer

thermal contact between the heater. The conversion coefficient in vacuum would give a result

that is overestimating the changing of temperature of the sample. It was therefore decided that

the thermal calibration coefficient measured in air be used for converting the temperature signal

in vacuum as well. A 40-second periodic noise was observed throughout the experiment in

vacuum. The conversion factor was measured as 0.124 V/℃, this was used for converting the

signal to temperature for the results in chapter 5. In the thermal map analysis, a 40-second noise

was also observed across the images. The thermal probe holder broke during the experiment

due to the heavy usage on the SThM. The probe holder was consequently improved by having

extra glue placed at the gold pin to increase the strength for secure the tip, however further

design improvements are desirable.

The thermal measurements showed that the retract changes of temperature are not consistent

for interpretation due to the effect of the adhesive force, therefore the approach temperature

should be used for interpreting the material properties. In the last discussion on the force curves,

a contamination layer of material was shown to affect the thermal curve as well. The

contamination layer could be oxidized material or a thin layer of liquid. This leads to a

discussion on the approach temperature. When there is a layer of material on the surface while

making the thermal measurement, the tip will first arrive at the contamination material before

reaching the sample, the contamination material can cause a change in temperature and provide

a misleading impression of the measurement. Thermal modelling, for example using a

simulation program such as COMSOL, is necessary to interpret multilayer effects.

118

The topography was measured on scan areas of 500nm x 500nm. A spatial resolution of

approximately 20nm for both the topography and thermal measurements was achieved. This

provides a much better spatial resolution for thermometry than traditional methods. The data

was repeated at three different points and three repeated measurements at each point. The idea

was to measure the variation of the measurements across the surface. The error on the adhesive

force and temperature has been shown to be small in general. However, for samples with a soft

surface such as PTFE, the roughness variation of 33% was shown to be large across the

different areas on the same scan indicating a large distribution in both adhesive force and

temperature measurements. Recording the change in tip temperature as the tip presses into the

sample also gives a measure of sample hardness, it has shown that for the soft surface, there is

a larger deformation temperature. The PTFE has shown a range 23-119% of deformation-

approach temperature ratio. The gold sample has shown to have a soft surface with the

deformation temperature of 39-75%.

The comparison between each sample was presented in both chapter 4 and 5, as well as a

comparison of measurements made in air and vacuum. The results showed that there is a 90%

heat loss of heat from the tip to the air in ambient conditions, whilst the losses are only about

10% in vacuum. This suggests that the vacuum environment can provide a better temperature

signal as the temperature difference between the tip and the sample is greater leading to a larger

temperature drop despite losing the solid-liquid conduction path. It was demonstrated across

all sample sets that the temperature drop in vacuum was greater than in air.

Silicon carbide was the hardest material from the sample set, and does have the highest thermal

conductivity. The mechanical and thermal properties gave consistent results in general,

however, the adhesive force was smaller than expected when compared to silicon and mica.

The change in temperature was also expected to have a higher value than observed, due to its

119

high thermal conductivity. The silicon carbide has a similar roughness to silicon, the average

height for the silicon carbide is 1.7nm while the silicon has 1.2nm. Both samples exhibited an

interference while measuring the topography.

The silicon gave the unusual shape when measuring the adhesive force which may be due to

the silicon oxide layer. The temperature drop was less consistent than the silicon carbide and

similar to mica. This may be a result of the additional layer of silicon oxide reducing the value

of thermal conductivity.

The PTFE is the softest material and had the lowest thermal conductivity from the sample set.

The soft surface of PTFE caused a large variation for both force and thermal measurements.

The adhesive force was shown to be low as expected. However, the PTFE showed the force

curves have shown an unusual shape in all environments. The possible reasons could be the

moisture left on the surface, or the sample surface deforming during the measurements.

Another possible reason is the PTFE absorbed the isopropanol that has applied for cleaning

however, further investigation would be required to test this. Although the deformation from

PTFE caused a big variation when measuring the approach temperature, the PTFE has the

lowest value of temperature drop for all environment.

The mica results were consistent being at the centre of each scale. The mica is expected to be

the cleanest sample, due to the layered structure, mica is cleaned by simply cleaving the top

layer. However, the surface features could not be seen from the topography because of the

smooth surface, only some features were detected in the vacuum topography measurements.

The thermal properties are similar to gold, and consistently larger than the PTFE.

The thin film gold is known to have a 150nm thickness, it is the targeted material for estimating

the thermal conductivity. The thin film gold surface was shown to be islanded due to the

120

evaporation process and appeared very different to the other bulk materials. Both the force and

thermal results are similar to mica, which implied that the range of thermal conductivity would

also be similar to mica. The curve of approach temperature against the thermal conductivity

was then plotted in chapter 5. The gold thin film thermal conductivity was estimated to be in

the range of 0.44 – 0.62 W/m⋅K. The thermal conductivity of thin film gold is expected to have

a smaller value to bulk material due to size effects.

This project has explored the use of SThM and provided an experimental procedure for

quantitative measurements using the SThM. There are some key results that could improve the

future development for the SThM at the University of York, and possible directions for future

research.

One of the key outcomes of this project is to examine the tip condition before performing any

experiment. This thesis has shown that the condition of the tip could vary during the experiment.

Using the SEM for inspection is suggested as a standard routine.

Most significantly, the vacuum environment was shown to provide a larger temperature drop

and has a potential to achieve higher resolution than air because of absence of water meniscus

formed. The flatter curve gives a more accurate representation of the sample change in

temperature. The pressure of the vacuum was left until it stabilized, it would be interesting to

see the effect on the same sample with different pressure.

When recording the temperature change, the experimenter should monitor the sample

temperature from the data logger. This thesis has shown that the sample can sometimes still be

cooling during the experiment adding an additional error, particularly in vacuum, where the

cooling paths are limited. In addition, it would be useful to mark the area on the sample for

reproducibility by returning to the same area.

121

The probe holder was shown to not be very robust under frequent use. The design of the holder

could be improved by following the similar design to the standard AFM holder, where a wire

is used to lock the tip position rather than slotting it in. This could reduce the chance for the

probe hitting the gold pin during the insertion process and improve the durability.

There are several areas that could possibly develop in the future from this research. The sample

selection could be expanded by including samples with thermal conductivity between mica and

silicon. This could provide more evidence for the relationship between the change in

temperature and thermal conductivity. The direction of using different materials as the tip

resistor would be an interesting research. The tip used in this project was a palladium resistor,

which has the thermal conductivity about 70W/m⋅K. From the results, the probe reached the

sensitivity limit when the sample thermal conductivity is similar or higher than the tip. If the

thermal conductivity of the tip material is increased, it could potentially increase the range of

materials which can be studied to higher thermal conductivity samples. The result has

highlighted the impact on the thermal transport measurements due to the material properties.

For example, the surface structure such as islands on a thin film, the dimensions such as bulk

material and thin film material all affect the measurements. The surface properties such as the

silicon oxide can also impact on the surface thermal properties. Modelling is needed to further

interpret the data, however there is a potential to apply the technique to study these effects.

In summary, this thesis has achieved the objectives for exploring the potential of using an

SThM for quantitative thermal measurements. If the points raised in this thesis are put into

practice, then the SThM can be successfully used to measure the thermal properties with a

spatial resolution of approximately 20nm, with the temperature resolution up to 0.01℃. The

range of thermal conductivities which can be measured is limited to the tip properties,

currently 70 W/m⋅K.

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